Question

Initially, there were only 197 weeds at a park. The weeds grew at a rate of 25% each week. The following function represents the weekly weed growth: f(x) = 197(1.25)x. Rewrite the function to show how quickly the weeds grow each day and calculate this rate as a percentage.

f(x) = 197(1.25)7x; grows at a rate of approximately 2.5% daily
f(x) = 197(1.257)x; grows at a rate of approximately 4.77% daily
f(x) = 197(1.03)x; grows at a rate of approximately 0.3% daily
f(x) = 197(1.03)7x; grows at a rate of approximately 3% daily

Answer 1

Answer:

  none of the above

  f(x) ≈ 197·1.03^x; approximately 3% daily

Step-by-step explanation:

If we let x represent days, then x/7 represents weeks and we can rewrite f(x) as ...

  f(x/7) = 197·1.25^(x/7) = 197·(1.25^(1/7))^x

  f(x) ≈ 197·1.03^x

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The daily multiplier of 1.03 represents a daily growth rate of

  1.03 -1 = .03 = 3%

_____

These answers are not found among the offered choices:

• f(x) = 197·1.03^x
• 3% daily growth

Answer 2

The correct answer to this question is D.