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

A

Step-by-step explanation:

i got it right on the test

Step-by-step answer:

The base of the exponential function is 1.29 for 7 days, as in

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

The new rate for days can be calculated by dividing x by 7 (where x remains the number of weeks), namely

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

Using the law of exponents, b^ (x/a) = b^ (x * (1/a)) = (b^ (1/a)) ^x

we simplify by putting b=1.29, a=7 to get

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

f (x) = 86 * (1.037) ^x since 1.29^ (1/7) evaluates to 1.037

Rounding 1.037 to 1.04 we get a (VERY) approximate function

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

1.04 is very approximate because 1.04^7 is supposed to get back 1.29, but it is actually 1.316, while 1.037^7 gives 1.2896, much closer to 1.29.