Question

A tree is 4 1/2 feet tall. It is expected to grow 1 3/4 feet per year. At this growth rate, how many years will it take for the tree to have a height greater then 40 feet?

Answer 1

21 years

Explanation:

Given

`Initial\ Height = 4(1)/(2)`

`Final\ Height = 40`

`Difference = 1(3)/(4)`

Required

Determine the years it'll take to grow to the final height

This question depicts arithmetic progression and will be solved using

`T_n = a + (n - 1)d`

Where

`T_n = 40`

`a = 4(1)/(2)`

`d = 1(3)/(4)`

Substitute these values in the given formula;

`40 = 4(1)/(2) + (n - 1)1(3)/(4)`

Convert all fractions to decimal

`40 = 4.5 + (n - 1) * 1.75`

Open Brackets

`40 = 4.5 + 1.75n - 1.75`

Collect Like Terms

`1.75n = 40 - 4.5 + 1.75`

`1.75n = 37.25`

Divide both sides by 1.75

`n = (37.25)/(1.75)`

`n = 21.2857142857`

`n = 21` (Approximated)