Question

Spencer plants a 7-inch tomato plant in his garden. The plant grows by about 15% per week for several months. Which formula represents the height h of the tomato plant (in inches) as a function of the time t in weeks since it was planted

Answer 1

`h(t) = 7(1.15)^(t)`

Explanation:

The equation for the plant's height after t weeks has the following format:

`h(t) = h(0)(1+r)^(t)`

In which h(0) is the initial height and r is the rate it increases per week, as a decimal.

Spencer plants a 7-inch tomato plant in his garden.

This means that
`h(0) = 7`

The plant grows by about 15% per week for several months.

This means that
`r = 0.15`. So

`h(t) = h(0)(1+r)^(t)`

`h(t) = 7(1+0.15)^(t)`

`h(t) = 7(1.15)^(t)`