Question

A 4 foot tree was planted in 2012 outside a high school. The tree grew continuously by 22% each year from that point. Find out what the height of the tree was in 2020.

Answer 1

The height of the tree in 2020 was of 19.63 feet.

Explanation:

Exponential equation for growth:

The exponential equation for the growth of an amount has the following format:

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

In which H(t) is the amount after t years, H(0) is the initial amount and r is the growth rate, as a decimal.

A 4 foot tree was planted in 2012 outside a high school.

This means that
`H(0) = 4`

The tree grew continuously by 22% each year from that point.

This means that
`r = 0.22`

Find out what the height of the tree was in 2020.

2020 is 2020 - 2012 = 8 years after 2012, so this is H(8).

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

`H(t) = 4(1+0.22)^t`

`H(4) = 4(1.22)^t`

`H(4) = 4(1.22)^8 = 19.63`

The height of the tree in 2020 was of 19.63 feet.