Question

A certain species of tree grows an average of 3.8 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 5 meters tall.

Answer 1

`n=500+8(n-1)`

DO NOT FORGET that the tree is already 5 meters tall on the FIRST WEEK, not the 0th week. So, f(x)=500+3.8x is incorrect.

(For example, on the second week the tree should be 503.8 meters tall. But if you plug 2 in f(x)=500+3.8x, you would get 507.6, which is the height of the tree on the third week.)

Answer 2

The answer is f(x) = 500 + 3.8x

The number of weeks is x. So, weekly, the tree grows 3.8x.
If the measurements of the growth begin when the tree started to grow, the equation would be: f(x) = 3.8x.
But, the measurements begin when the tree is 5 m tall. Since 1 m is 100 cm, this means that 5 m is 500 cm. Thus, the equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 5 meters tall is:
f(x) = 500 + 3.8x