4
advanced-math

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

B

160 acres

C

320 acres

D

80 acres

Correct Answer: A

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)d−1A(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.

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Set 34: Exponential Functions 34