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.

Answer 1

`f(x) = 86(1.0257)^(x)`

Explanation:

The growth of the function after t days can be modeled by the following function:

`f(x) = f(0)(1 + (r)/(7))^(x)`

In which f(0) is the initial value and r is the weekly rate. Since a week has 7 days, to find the equation for the daily growth, we divide by 7.

In this question:

We have that
`f(0) = 86, r = 0.18`

So

`f(x) = f(0)(1 + (r)/(7))^(x)`

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

`f(x) = 86(1.0257)^(x)`