How do I do this problem

Question

Your company purchases a truck for $60,000 that is worth $22,800 after 6 years. Find the

average rate of change. Then write a linear function f(x) for the value f of the truck after

x years. Find the inverse function f^-1(x) of f. Then find and interpret f^−1(35,200).

Answer 1

22,800=60,000-6x where d = absolute annual rate of change

6d = 60000-22800= 37200

d = 37,200/6 = $6200 annual decrease per year

percent rate of change per year = r = -6200/60,000

= -62/600 =-10 1/3% annual rate of change

value of the truck after x years = f(x) = 60,000 - 6200x

to find the inverse function switch x and y

y =60,000-6200x

x =60,000-6200y

solve for the new y = f^-1(x)

6200y = 60000-x

y = f^-1(x) = 60,000/6200 - t/6200 = 300/31 -t/6200

f^-1(35200) = 300/31 - 35,200/6,200 = 300/31 - 176/31 = 124/31 = 4

= 4 years for the truck to decline in value to $35,200 from $60,000

f(4)=60000-6200(4)= 60000-24800= 35200