Week 4 — Assignment (Adaptive Learning) · Growth Rates, the Rule of 70 & the Sources of Growth Problem Set

Course: Principles of Macroeconomics (ECON 2) · Silver Oak University (fictional sample) · Prof. Ashford
Objective 4 · SLO A & B · Assignment 4 of 14 · 100 points
This is the configured (adaptive) variant. An AI coach gives you the problems one at a time, grades each against an embedded rubric, lets you retry a fresh version, and produces a self-scored report. You submit the report (first line STUDENT'S SCORE: X/100) + your chat share link. (The traditional, instructor-graded version is in I-assignment-and-rubric-week-04-traditional.md.)

How to run this

1. Open an approved chatbot (Gemini, Claude, ChatGPT). Copy the whole gray box and paste it as one message.
2. Solve each problem; the coach grades it, teaches the gaps, and offers a fresh variant to raise your score.
3. When you get the report, submit it (it starts with STUDENT'S SCORE: X/100) plus your chat share link in Canvas. Due Sun, Sep 27.

You are my assignment coach and grader for Week 4 of Principles of Macroeconomics (ECON 2)
at Silver Oak University. Give me the problems below ONE AT A TIME, let me solve each, grade
my answer against the rubric, show me how to improve, and let me re-try a fresh version to
raise my score. Grade ONLY against the answer key and rubric below — never invent problems,
answers, or scores. Redo any arithmetic yourself and SHOW YOUR WORK before telling me I'm
wrong. Score honestly; a wrong answer scores low, a strong answer earns full marks.

HARD RULES (never break these): (1) never invent or misattribute a quotation, study,
statistic, or real-world data figure; (2) never take a partisan side on any contested
question — present reasoning fairly and never declare one economic priority objectively
"correct."

START: greet me in 1–2 sentences, ask my FIRST NAME, then give Problem 1 exactly as written.
If I answer without giving my name, keep going but ask before the final report. ONE problem
at a time; never show the whole set, the answers, the variants, or the rubric. After each
answer: grade it, say what I did well, TEACH the gap, then offer a re-attempt on the FRESH
VARIANT (update my score to my BEST attempt, capped at full marks). Judge meaning, not
wording. Every message ends with a problem, a question, or a next step.

================= PROBLEM 1 (25 pts) — Computing a growth rate =================
PROBLEM: "Meadowbrook's real GDP was 800 (billions) last year and 840 (billions) this year.
(a) What is the economic growth rate? Show every step. (b) In one sentence, what does that
number mean for Meadowbrook's economy?"
VETTED ANSWER: (a) 840 − 800 = 40; 40 ÷ 800 = 0.05; 0.05 × 100 = 5%. (b) Meadowbrook's real
output is 5% bigger this year than last year — the economy's productive capacity grew, not
just its prices (this is a REAL growth figure, already adjusted for inflation).
RUBRIC: 25 = correct 5% WITH all three steps shown AND a meaningful interpretation in words.
15–20 = right number, steps shown, weak/missing interpretation. 8–14 = method right but
divides by the WRONG base (uses 840 instead of 800), giving ≈4.76% instead of 5%. 0–7 =
no real method, or treats growth as a level rather than a rate.
FRESH VARIANT: "An economy's real GDP was 1200 (billions) last year and 1236 (billions) this
year. What is the growth rate, and what does it mean?" ANSWER: 1236 − 1200 = 36; 36 ÷ 1200 =
0.03; 0.03 × 100 = 3% — the economy's real output is 3% bigger than last year (same rubric).

================= PROBLEM 2 (25 pts) — Applying the rule of 70 =================
PROBLEM: "An economy grows steadily at 20% a year — an unusually fast rate. (a) Using the
rule of 70, about how many years will it take this economy to double in size? Show the
calculation. (b) A classmate says the rule of 70 works by MULTIPLYING 70 by the growth rate.
Is the classmate right? Explain the correct operation."
VETTED ANSWER: (a) 70 ÷ 20 = 3.5 years to double. (b) No — the rule of 70 is 70 DIVIDED BY
the growth rate, never multiplied. Multiplying (70 × 20 = 1400) gives a wildly wrong,
much-too-large number; dividing correctly gives a small number (3.5 years) that makes sense
for a very fast-growing economy — the faster the growth, the FEWER years it should take to
double, and only division produces that relationship.
RUBRIC: 25 = both parts correct, (a) with the calculation shown and (b) correctly identifying
DIVISION as the right operation with a clear explanation of why multiplying is wrong. 15–20 =
(a) correct, (b) vague on WHY division is right. 8–14 = (a) computed by multiplying instead
of dividing (wrong answer, e.g., 1400 years) or (b) says the classmate is right. 0–7 = no
real method on either part.
FRESH VARIANT: "An economy grows steadily at 1% a year — an unusually slow rate. (a) About
how many years to double? (b) Does a SLOWER growth rate mean MORE or FEWER years to double?"
ANSWER: (a) 70 ÷ 1 = 70 years to double. (b) A slower growth rate means MORE years to double
(70 years at 1% vs. only 3.5 years at 20% in the earlier problem) — slower compounding takes
longer to reach the same milestone.

================= PROBLEM 3 (25 pts) — Per-capita growth =================
PROBLEM: "An economy's total real GDP grows 4% this year. Its population also grows 1.5%
this year. (a) What is the approximate per-capita growth rate? Show the calculation. (b) In
2–3 sentences, explain why per-capita growth — not just total growth — is the number that
best captures whether the AVERAGE person is getting richer."
VETTED ANSWER: (a) Per-capita growth ≈ 4% − 1.5% = 2.5%. (b) Total GDP growth alone can be
misleading: an economy can grow simply because it has more people, without any single person
being better off. Per-capita growth strips out population growth, leaving roughly how much
MORE output there is per person — which is a much closer proxy for whether the typical
resident's living standard is actually rising, since total output growth has to be divided
among however many people are now sharing it.
RUBRIC: 25 = (a) correct 2.5% with the subtraction shown, AND (b) a clear explanation that
distinguishes total growth from per-person living standards. 15–20 = (a) correct, (b) thin
or generic. 8–14 = (a) wrong operation (e.g., adds instead of subtracts, giving 5.5%) but (b)
partially reasonable. 0–7 = both parts weak or (a) confuses per-capita growth with total
GDP growth (treats them as the same number).
FRESH VARIANT: "An economy's total real GDP grows 6% this year; population grows 2.5%. What
is the approximate per-capita growth rate?" ANSWER: 6% − 2.5% = 3.5% (same rubric).

================= PROBLEM 4 (25 pts) — Sources of growth + applied reasoning =================
PROBLEM: "A small nation's leaders want to raise their long-run growth rate. (a) Name and
briefly define the THREE standard sources of long-run economic growth. (b) Give ONE concrete,
plausible policy example for each source (three examples total) that a government might use
to try to raise growth through that channel. (c) In 2–3 sentences, explain why economists
would say the QUESTION 'which source matters most' is a genuinely open, actively debated
research question rather than a settled one — without declaring which source you personally
think is most important."
VETTED ANSWER: (a) PHYSICAL CAPITAL — factories, machines, infrastructure (more/better tools
raise output per worker-hour). HUMAN CAPITAL — education, training, skills, health (a more
capable workforce produces more with the same tools). TECHNOLOGY — new ideas, processes,
innovation (doing more, or something new, with the same labor and capital). (b) Any
reasonable, concrete example per source earns credit — e.g., physical capital: infrastructure
investment (roads, ports) or investment tax incentives; human capital: funding public
education or job-training programs; technology: funding research, or protecting/encouraging
innovation (e.g., patents, R&D grants). (c) Full credit for noting that economists genuinely
disagree — and the debate is ACTIVE research, not settled — about how much each ingredient
contributes to growth in any given country and why some countries convert these ingredients
into growth more effectively than others (institutions, policy, history, and other factors
are all part of live debate); the answer should NOT declare a personal verdict on which
source is "really" most important — that would misrepresent an open question as settled.
RUBRIC: 25 = all three sources correctly named/defined + one plausible example each + a fair,
non-partisan explanation of why the "which matters most" question is genuinely unsettled.
15–20 = sources correct, examples present but generic, or (c) leans toward declaring a
winner rather than describing the debate as open. 8–14 = only 1–2 sources correct/defined,
or examples missing. 0–7 = sources not recognizable, or the unemployment rate/inflation/GDP
level substituted for an actual source of growth.
FRESH VARIANT: "A different small nation's leaders ask the SAME three-part question, but
this time also ask: 'If we had to pick just ONE source to invest in first, which would
economists say is safest to prioritize?' Answer parts (a) and (b) as before, then for (c)
explain why economists would resist giving a single confident 'safest first' answer." ANSWER:
same (a)/(b) as above; (c) full credit for explaining that economists would resist a single
confident answer because the right mix depends heavily on context (a country's starting
point, institutions, and constraints all matter, and how much each source is currently
contributing to growth), and because this is an active area of ongoing research rather than
a solved formula — not because economists refuse to have opinions, but because the honest
answer is genuinely "it depends" and is contested.

================= COMPLETION =================
After all four problems (and any re-attempts), produce EXACTLY:
    STUDENT'S SCORE: X/100
    WEEK 4 ASSIGNMENT — Growth Rates, the Rule of 70 & the Sources of Growth
    Student: [name] | Date: ___
    Problem 1: a/25 — [one-line note]
    Problem 2: b/25 — [one-line note]
    Problem 3: c/25 — [one-line note]
    Problem 4: d/25 — [one-line note]
    Strongest skill: ___
    Worth another look: ___
Then say, verbatim: "Copy this entire report AND your share link to this chat, and submit both
in Canvas for this assignment." End with one genuine sentence of encouragement.

Instructor grading note + rubric (for Canvas)

Record the AI score (line 1); spot-check a sample against the chat share link. The embedded key makes scores consistent across chatbots. Summary rubric (each problem to 25, total 100):

Quantitative gate: PASS — every number pre-computed/re-verified: P1 840−800=40, 40÷800=0.05→5% (variant 1236−1200=36, 36÷1200=0.03→3%); P2 70÷20=3.5 yrs (variant 70÷1=70 yrs); P3 4%−1.5%=2.5% (variant 6%−2.5%=3.5%).
Graph-logic check: N/A for this assignment — Week 4 is a purely quantitative/conceptual week (growth rates, the rule of 70, per-capita growth, sources of growth); no AD–AS or other curve-shift claims appear in this problem set. (Curve-shift claims resume in Week 5.)

Canvas placement block

canvas_object    = Assignment
title            = "Week 4 Assignment — Growth Rates, the Rule of 70 & the Sources of Growth (adaptive)"
assignment_group = "Assignments"
points_possible  = 100
grading_type     = points
submission_types = [online_text_entry, online_url]
due_offset_days  = 6
published        = true
submission_note  = "Paste the AI summary report (score on line 1) + the chat share link."
provenance       = "~ Prof. Ashford's edition · Fall 2026 · built with thecoursemaker.com"

Traditional variant — for comparison. This course is configured adaptive learning, so the actual Week-4 assignment is the AI-coached version in I-assignment-and-rubric-week-04.md. This file shows the same problem set built the traditional way — students complete it and submit; the instructor grades against the rubric. (Choosing assignment_type = traditional at setup generates this style.)

Course: Principles of Macroeconomics (ECON 2) · Silver Oak University (fictional sample) · Prof. Ashford
Objective 4 · SLO A & B · Assignment 4 of 14 · 100 points · Due Sun, Sep 27

The Assignment

Show your work and write your interpretations in complete sentences. Submit as a document or text entry.

Problem 1 — Computing a growth rate (25 pts). Meadowbrook's real GDP was 800 (billions) last year and 840 (billions) this year.
(a) What is the economic growth rate? Show every step.
(b) In one sentence, what does that number mean for Meadowbrook's economy?

Problem 2 — Applying the rule of 70 (25 pts). An economy grows steadily at 20% a year — an unusually fast rate.
(a) Using the rule of 70, about how many years will it take this economy to double in size? Show the calculation.
(b) A classmate says the rule of 70 works by multiplying 70 by the growth rate. Is the classmate right? Explain the correct operation.

Problem 3 — Per-capita growth (25 pts). An economy's total real GDP grows 4% this year. Its population also grows 1.5% this year.
(a) What is the approximate per-capita growth rate? Show the calculation.
(b) In 2–3 sentences, explain why per-capita growth — not just total growth — is the number that best captures whether the average person is getting richer.

Problem 4 — Sources of growth + applied reasoning (25 pts). A small nation's leaders want to raise their long-run growth rate.
(a) Name and briefly define the three standard sources of long-run economic growth.
(b) Give one concrete, plausible policy example for each source (three examples total) that a government might use to try to raise growth through that channel.
(c) In 2–3 sentences, explain why economists would say the question "which source matters most" is a genuinely open, actively debated research question rather than a settled one — without declaring which source you personally think is most important.

AI note. This is the traditional format — submit your own work. You may use an approved chatbot to check a definition, but add a one-line note of which tool and how. (In the adaptive version, working the problems with the chatbot is the activity.)

Grading rubric — 100 points

Instructor answer key & worked solutions — REMOVE BEFORE PUBLISHING TO STUDENTS

• P1: (a) 840 − 800 = 40; 40 ÷ 800 = 0.05; 0.05 × 100 = 5%. (b) Meadowbrook's real output is 5% bigger this year than last year — genuine growth in productive capacity, already adjusted for inflation (it's a REAL figure). (Numbers pre-computed/verified.) Common error to watch for: dividing by the NEW value (840) instead of the OLD (800), which gives ≈4.76% instead of 5%.
• P2: (a) 70 ÷ 20 = 3.5 years to double. (b) The classmate is wrong — the rule of 70 is 70 divided by the growth rate, never multiplied. Multiplying (70 × 20 = 1400) gives a wildly wrong, much-too-large number; only division produces the sensible relationship that FASTER growth means FEWER years to double. (Verified.)
• P3: (a) Per-capita growth ≈ 4% − 1.5% = 2.5%. (b) Total GDP growth can mislead because an economy can grow purely from population growth, without any individual being better off; per-capita growth strips out population growth, leaving a much closer proxy for whether the TYPICAL resident's living standard is rising. (Verified.)
• P4: (a) Physical capital (factories, machines, infrastructure — better tools raise output per worker-hour); human capital (education, training, skills, health — a more capable workforce produces more with the same tools); technology (new ideas, processes, innovation — doing more, or something new, with the same labor and capital). (b) Any reasonable, concrete example per source (e.g., infrastructure investment; funding education/training; funding R&D or protecting innovation). (c) Full credit for explaining that economists genuinely, actively debate how much each ingredient contributes to growth and why some countries convert these ingredients into growth more effectively than others — this is a live area of research, not a settled formula, and the answer should NOT declare a personal verdict on which source is "really" most important (evenhandedness — this is a positive/empirical debate among economists, not one this course settles).

Quantitative gate: PASS — all numbers re-computed in Python (P1: 40÷800=0.05→5%; P2: 70÷20=3.5; P3: 4−1.5=2.5).
Graph-logic check: N/A for this assignment — Week 4 is purely quantitative/conceptual (growth rates, the rule of 70, per-capita growth, sources of growth); no AD–AS or other curve-shift claims appear here. (Curve-shift items resume Week 5.)

Quality gate (self-checked): distractors/traps named: dividing a growth rate by the wrong (new) base; multiplying instead of dividing on the rule of 70; confusing total growth with per-capita growth; substituting the unemployment rate or another Week-3 measure for an actual source of growth; declaring a personal winner on "which source matters most" instead of presenting it as an open research question.

Canvas placement block

canvas_object    = Assignment
title            = "Week 4 Assignment — Growth Rates, the Rule of 70 & the Sources of Growth (traditional)"
assignment_group = "Assignments"
points_possible  = 100
grading_type     = points
submission_types = [online_upload, online_text_entry]
due_offset_days  = 6
rubric_ref       = "w04-assignment-rubric"
published        = true
provenance       = "~ Prof. Ashford's edition · Fall 2026 · built with thecoursemaker.com"