Question

Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 18% each week. The following function represents the weekly weed growth: f(x) = 86(1.18)x. Rewrite the function to show how quickly the weeds grow each day. f(x) = 86(1.02)x; grows approximately at a rate of 0.2% daily f(x) = 86(1.18)7x; grows approximately at a rate of 1.8% daily f(x) = 86(1.02)7x; grows approximately at a rate of 2% daily f(x) = 86(1.187)x; grows approximately at a rate of 0.18% daily

Answer 1

Correct option: third one

f(x) = 86(1.02)7x; grows approximately at a rate of 2% daily

Explanation:

We can rewrite the equation using the model:

P = Po * (1 + r/n) ^ (nt)

Where P is the final value, Po is the inicial value, r is the rate, t is the time and n is the relation of the rate and the time (in our case, the rate is weekly and the time will be in days, so n = 7)

With P = f(x), Po = 86, r = 0.18 and t = x, we have:

f(x) = 86 * (1 + 0.18/7) ^ (7x)

f(x) = 86 * (1.02) ^ (7x)

So the daily rate of growth is approximately 2%

Correct option: third one