7

Set 1: Exponential Functions

Explanation

Answer: A

A forest fire spreads exponentially. It covers 10 acres on day 1, 40 acres on day 2. How many acres on day 4?

A.

640 acres

✓ Correct
B.

160 acres

C.

320 acres

D.

80 acres

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Find the pattern and extend. 1. Growth Factor: 4010=4\frac{40}{10} = 4 per day. 2. Formula: A(d)=10(4)d1A(d) = 10(4)^{d-1} where dd is the day. 3. Day 4: A(4)=10(4)3=10(64)=640A(4) = 10(4)^3 = 10(64) = 640 acres. Strategic Tip: From day to day, multiply by the growth factor. Choice B is incorrect because this is day 3: 10(4)2=16010(4)^2 = 160. Choice C is incorrect because this doesn't match the pattern. Choice D is incorrect because this underestimates growth.

Key Steps:

The correct answer is 640 acres

Why others are wrong:
B: Choice B 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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