High School

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 :

The correct answer to this question is D

Answer:

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

Step-by-step 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

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