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.

A.) f(x) = 197(1.25)^7x; grows at a rate of approximately 2.5% daily
B.) f(x) = 197(1.25^7)^x; grows at a rate of approximately 4.77% daily
C.) f(x) = 197(1.03)^x; grows at a rate of approximately 0.3% daily
D.) f(x) = 197(1.03)^7x; grows at a rate of approximately 3% daily

Answer 1

The correct answer to this question is D

Answer 2

D.) f(x) = 197(1.03)^(7x); grows at a rate of approximately 3% daily

Explanation:

The growth equation can be written in terms of a rate compounded 7 times per week:

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

f(x) ≈ 197×1.0324^(7x) . . . . x represents weeks, a daily growth factor is shown

The daily growth rate as a percentage is the difference between the daily growth factor and 1, expressed as a percentage:

(1.0324 -1) × 100% = 3.24%

The best match is choice D:

f(x) ≈ 197(1.03^(7x)); grows approximately 3% daily