Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 29% each week. The following function represents

Question

2 months ago

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Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 29% each week. The following function represents

the weekly weed growth: f(x) = 86(1.29)x. Rewrite the function to show how quickly the weeds grow each day.
A.f(x) = 86(1.04)x; grows approximately at a rate of 0.4% daily
B.f(x) = 86(1.04)7x; grows approximately at a rate of 4% daily
C.f(x) = 86(1.29)7x; grows approximately at a rate of 20% daily
D.f(x) = 86(1.297)x; grows approximately at a rate of 2% daily

Mathematics

2 answers:

AnnZ [12.3K] · Answer 1 · 2026-03-19T14:14:03+03:00

Step-by-step answer:

The base of the exponential function is set at 1.29 for a period of 7 days, which is expressed as

f(x) = 86*(1.29)^x

To determine the daily rate, divide the variable x by 7 (keeping x as the number of weeks), resulting in

f(x) = 86*1.29^(x/7)

Applying the exponent rule, b^(x/a) = b^(x*(1/a)) = (b^(1/a))^x

we can simplify by setting b=1.29, a=7 to arrive at

f(x) = 86*(1.29^(1/7))^x

f(x) = 86*(1.037)^x since evaluating 1.29^(1/7) yields approximately 1.037

Rounding 1.037 to 1.04 gives a (VERY) rough estimate function

f(x) = 86 * (1.04^x)

1.04 is only an approximation because 1.04^7 is expected to return 1.29, it actually results in 1.316; meanwhile, 1.037^7 returns 1.2896, which is much closer to 1.29.

lawyer [12.5K] · Answer 2 · 2026-03-19T14:15:48+03:00

lawyer [12.5K]2 months ago

7 0

Answer:

A

Detailed explanation:

I answered correctly on the test