Question

One year after you buy a tree, it is 10 feet tall. Each year after you buy the tree, it grows 2 feet. Write a function that represents the arithmetic sequence (1,10),(2,12),(3,14). How long does it take for the tree to reach its maximum height of 28 feet?

Answer 1

10 years

Explanation:

We are told that One year after you buy a tree, it is 10 feet tall. Thus, it's initial height after 1 year is 10 ft.

Now we are told that each year after you buy the tree, it grows 2 feet. This means that it's height after you bought it was; f(0) = 10 - 2 = 8ft

Thus,

f(1) = 8 + 2 = 10

f(2) = 8 + 2 + 2 = 12

f(3) = 8 + 2 + 2 + 2 = 14

The pattern here is;

f(x) = 8 + 2x

Where x is number of years

Thus, for it to reach a maximum height of 28 ft;

28 = 8 + 2x

Subtract 8 from both sides to give;

28 - 8 = 2x

2x = 20

x = 20/2

x = 10 years