A function is f(n) and The tree reaches its maximum height of 28 feet-------- years after you buy the tree.

Question

One year after you buy a tree, it is 12 feet tall. Each year after you buy the tree, it grows 4 feet. Write a function that represents the arithmetic sequence. How long does it take for the tree to reach its maximum height of 28 feet?

Please answer

Answer 1

n = time, in years

f = height, a function depending solely on time, given in years

f(n=1 year) = 12 feet

since the tree grows 4 feet per year, we know you bought the tree one year previously, so:

f(n= 0 years) = 12 - 4 feet = 8 feet

this is our y-intercept, or in the common form f(x) = ax + b , our 'b' value. Our 'a' value is the growth rate: 4 (feet/year) [feet per year]. Now we have everything we need to set up the equation:

f(n) = 4n + 8 feet

we want to solve for the time 'n' when f(n) = 28 feet:

28 feet = 4n + 8 feet

28 - 8 feet = 4n + 8 - 8 feet (minus 8 from both sides to combine our constant terms)

20 feet = 4n

20/4 = 4n/4 (divide both sides by 4 to isolate 'n')

5 years = n (I have omitted the units to perserve space and clarity, since

the 4 has units of feet/year, feet will cancel and we are left with n, in years)