help! (please) i need to understand this for finals! thanks in advance!

Question

a 2 foot tall tree is planted and then grows at a rate of 3 feet per year for 40 years. find a linear function that models the growth of this tree. sketch its graph. interpret its slope and y-intercept. use your function to find the height of the tree at 7 years 4 months and to find the age (years since planting) of the tree when it is 100 feet tall

Answer 1

One way to solve this (Math problems are usually solved in many ways):

 

Year    Height

0          2  (initial)

1          2+3 =5

2          (2+ 3) + 3 = 2+ 3*2 = 8

3          2 +3 + 3+ 3 =2 + 3*3= 11

4          2 + 3*4 = 14 (see the pattern?)

 

and so on, so that at Year X, the height is 2 + 3*X , i.e. H=2+3X

 

intercept =2, initial height

slope=3 , rate of increase in height per year ( 3 ft/yr)

 

Do the rest.