2

Set 17: Exponential Functions

Explanation

Answer: B

An investment grows according to A(t)=1000(1.07)tA(t) = 1000(1.07)^t. What is the annual growth rate?

A.

1.07%

B.

7%

✓ Correct
C.

107%

D.

0.07%

Detailed Explanation

Choice B is correct. Choice B is the correct answer. The rate is found from the factor b=1+rb = 1+r. 1. Identify Factor: b=1.07b = 1.07. 2. Solve for r: 1+r=1.07  ⟹  r=0.071+ r = 1.07 \implies r = 0.07. 3. Convert: 0.07=7%0.07= 7\%. Strategic Tip: Subtract 1 from the base to get the rate as a decimal. Choice A is incorrect because it confuses the decimal with the percentage. Choice C is incorrect because 107% would mean b=2.07b=2.07. Choice D is incorrect because 0.07% is 0.00070007.

Key Steps:

•

The correct answer is 7%

Why others are wrong:
A: Choice A is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.
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