Week 13 Quiz

Which table of outputs, for the inputs 0, 1, 2, 3, has a constant ratio, the pattern of an exponential function?

Select one.

• 4, 7, 10, 13
• 3, 6, 12, 24
• 3, 6, 9, 12
• 4, 8, 12, 16

In the exponential function f(x) = 3 · 2ˣ, what is the initial value, the output at x = 0?

Select one.

• 3
• 2
• 6
• 0.375

Evaluate f(2) for f(x) = 3 · 2ˣ.

Select one.

• 36
• 6
• 12
• 10

Evaluate f(−2) for f(x) = 3 · 2ˣ.

Select one.

• −12
• 0.75
• −0.75
• 1.5

For f(x) = 3 · 2ˣ, the output at x = −2 is only 0.75. Which statement about growth or decay is correct?

Select one.

• Decay, because 0.75 is less than the initial value 3
• Growth, because the base 2 is greater than 1
• Decay, because the input −2 is negative
• Neither, because 0.75 is not a whole number

A 100-gram sample halves every period, so A(t) = 100 · (1 ⁄ 2)ᵗ with t in half-lives. How much remains after 3 half-lives?

Select one.

• 50 grams
• 33.3 grams
• 6.25 grams
• 12.5 grams

Which statement describes the graph of f(x) = 3 · 2ˣ?

Select one.

• It crosses the y-axis at (0, 3) and approaches the x-axis on the left without touching it
• It crosses the y-axis at (0, 2) and approaches the x-axis on the left without touching it
• It crosses the y-axis at (0, 3) and crosses the x-axis at a negative input
• It crosses the y-axis at (0, 6) and approaches the line y = 3 on the left

A town of 800 people grows 3% per year. Which growth factor b belongs in the model P(t) = 800 · bᵗ?

Select one.

• 0.03
• 3
• 1.03
• 0.97

1,000 dollars earns 6% interest compounded annually. What is the balance after 2 years?

Select one.

• 1,120.00 dollars
• 1,060.00 dollars
• 1,191.02 dollars
• 1,123.60 dollars

Select every true statement about the natural base e.

Select every option that applies.

• e is about 2.71828
• e is irrational, like π
• e is a variable you solve for in each problem
• e equals 2.7 exactly
• As n grows, (1 + 1 ⁄ n)ⁿ levels off toward e

1,500 dollars earns 5% interest compounded continuously, so A = 1500 · e^(0.05 · 4) after 4 years. Using e^0.2 ≈ 1.2214, what is the balance?

Select one.

• 1,832.10 dollars
• 1,800.00 dollars
• 1,823.26 dollars
• 1,575.00 dollars