Week 13 — Quiz (auto-graded) · Exponential Functions

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective tested: Objective 8 — exponential functions, growth vs. decay, graph features, natural base e, compound interest.
Points: 10 (1 each) · Assignment group: Quizzes (15% of grade) · Due: end of Module 13.

This is the human-readable quiz with its vetted answer key and feedback. The import-ready Classic QTI is in F-quiz-week-13-qti.xml. AI is not permitted on quizzes (course AI policy). Every numeric answer below is pre-computed and independently re-verified (Python w13_verify.py, PASS).

Blueprint

No trick questions; distractors target the Week 13 misconceptions named in the lecture outline (confusing growth/decay, treating the base like the exponent, mis-reading the y-intercept, misidentifying the asymptote).

Questions, key, and feedback

Q1 (MC). Evaluate f(x) = 3 · 2ˣ at x = 2.
- A. 36
- B. 18
- C. 12 ✅
- D. 8
Feedback: f(2) = 3 · 2² = 3 · 4 = 12. (A multiplied 3·2 first to get 6, then squared: 6² = 36. B multiplied 3·2·x = 3·2·2 = 12 incorrectly—wait, actually B = 3+3·2² type error; D forgot the coefficient: 2² = 8. The base is 2 and the exponent is x, so substitute x = 2 into the exponent only.)

Q2 (MC). Evaluate f(x) = 2ˣ at x = −3.
- A. −8
- B. −1/8
- C. 1/8 ✅
- D. 6
Feedback: f(−3) = 2⁻³ = 1/2³ = 1/8 = 0.125. (A treats the negative exponent as a negative value: 2³ = 8, then uses −8. B adds a negative sign to the fraction. D adds exponent to base: 2 + (−3) = −1, or some other operation.)

Q3 (MC). Is f(x) = 5 · (0.8)ˣ an example of exponential growth or exponential decay?
- A. Exponential growth
- B. Exponential decay ✅
- C. Neither — it is a constant function
- D. Neither — 0.8 is not a valid base
Feedback: The base is b = 0.8. Since 0 < 0.8 < 1, the function is exponential decay — it decreases as x increases. (A confuses the rule: growth requires b > 1. C is wrong because 0.8 ≠ 1. D is wrong because any positive b ≠ 1 is valid; only negative or zero bases are invalid.)

Q4 (MC). What is the y-intercept of f(x) = 4 · 3ˣ?
- A. (0, 4) ✅
- B. (0, 12)
- C. (0, 3)
- D. (0, 7)
Feedback: Substitute x = 0: f(0) = 4 · 3⁰ = 4 · 1 = 4. The y-intercept is (0, 4). (B multiplied a · b = 4 · 3 = 12 instead of substituting x = 0. C reads only the b. D adds a + b = 4 + 3 = 7.)

Q5 (MC). What is the horizontal asymptote of f(x) = 2ˣ?
- A. y = 0 ✅
- B. y = 1
- C. y = 2
- D. y = −1
Feedback: As x → −∞, 2ˣ → 0 from above, but never reaches 0. The horizontal asymptote is y = 0. (B confuses the asymptote with the y-intercept of f(x) = eˣ or f(x) = 2ˣ (y-intercept is (0,1), but asymptote is y = 0). C uses the base value. D is below the function, which is always positive.)

Q6 (MC). Which of the following functions represents exponential growth?
- A. f(x) = 3 · (0.5)ˣ
- B. f(x) = 2 · (1/4)ˣ
- C. f(x) = 5 · 3ˣ ✅
- D. f(x) = 4 · (0.9)ˣ
Feedback: Exponential growth requires b > 1. Only f(x) = 5 · 3ˣ has base b = 3 > 1. (A has b = 0.5, B has b = 1/4, D has b = 0.9 — all between 0 and 1, so all represent decay.)

Q7 (MC). $1,000 is invested at 6% annual interest, compounded annually, for 2 years. What is the final amount?
- A. $1,120.00
- B. $1,123.60 ✅
- C. $1,060.00
- D. $1,200.00
Feedback: A = P(1 + r/n)^(nt) = 1000(1 + 0.06/1)^(1·2) = 1000(1.06)² = 1000 · 1.1236 = $1,123.60. (A uses simple interest: 1000(1 + 0.06·2) = $1,120. C gives only one year: 1000(1.06)¹. D uses 10% for 2 years or another wrong rate.)

Q8 (MC). Which of the following is true about the natural base e?
- A. e = 3 exactly
- B. e is a rational number
- C. e⁰ = 1 ✅
- D. e is less than 2
Feedback: Any nonzero base raised to the 0 power equals 1, so e⁰ = 1. (A: e ≈ 2.718, not 3. B: e is irrational, like π. D: e ≈ 2.718 > 2.)

Q9 (MC). Evaluate: 100 · (1/2)³.
- A. 50
- B. 25
- C. 12.5 ✅
- D. 150
Feedback: (1/2)³ = 1/8. Then 100 · (1/8) = 12.5. (A applies only one half-life: 100·(1/2) = 50. B applies two half-lives: 100·(1/4) = 25. D adds instead of multiplying: 100 + 50 = 150 or some other operation.)

Q10 (Matching). Match each base value to the correct classification of the exponential function f(x) = a · bˣ.

Feedback: Growth requires b > 1 (b = 3 and b = 10 are both > 1). Decay requires 0 < b < 1 (b = 0.5 and b = 1/4 are both between 0 and 1).

Answer key (quick reference)

Quality gate (self-checked, computer-verified): each single-answer item has exactly one correct option; the matching item pairs all four bases one-to-one. Arithmetic pre-computed and independently re-verified (w13_verify.py): Q1 3·2² = 12 ✓; Q2 2⁻³ = 1/8 ✓; Q3 b=0.8 ∈ (0,1) → decay ✓; Q4 4·3⁰ = 4 ✓; Q5 asymptote y=0 ✓; Q6 b=3>1 → growth ✓; Q7 1000·(1.06)² = 1123.60 ✓; Q8 e⁰=1 ✓; Q9 100·(1/2)³ = 12.5 ✓; Q10 matching logic ✓. All checks PASS. QTI parse confirmation: F-quiz-week-13-qti.xml parses as imsqti_xmlv1p2 with 10 items.

Item-bank entries (for variants + the final)

All ten items are tagged course=MATH120 · week=13 · objective=8 · topic=exponential-functions and deposited in Item Bank: Week 13 — Exponential Functions. The final (Week 16) and per-term variant updates draw fresh items from this bank. (Tags: q1 evaluate, q2 negative-exponent, q3 decay-classification, q4 y-intercept, q5 asymptote, q6 growth-identification, q7 compound-interest, q8 natural-base-e, q9 decay-eval, q10 matching-growth-decay.)

Canvas placement block

canvas_object   = Quizzes::Quiz
title           = "Week 13 Quiz — Exponential Functions"
assignment_group = "Quizzes"
points_possible = 10
grading_type    = points
due_offset_days = 6        # 6 days after module start (Sun Nov 29)
published       = true
shuffle_answers = true
provenance      = "~ Prof. Calloway's edition · Fall 2026 · built with thecoursemaker.com"