A new 2014 luxury sedan that sold for $38,880 has a book value V of $24,319 after t = 2 years.

Question

(a) Find a linear model for the value V of the sedan.

V(t) =

(b) Find an exponential model for the value V of the sedan. Round the numbers in the model to four decimal places.

V(t) =

(c) Use a graphing utility to graph the two models in the same viewing window.

(d) Which model represents a greater depreciation rate in the first year?

1. linear model
2. exponential model

(e) For what years is the value of the sedan greater using the linear model? the exponential model? (Round your answers to the nearest integer. Enter your answers using interval notation.)

linear model:

exponential model:

Answer 1

So you have 2 points (0,38,880) and ( 2, 24,319). For linear decay we have a straight line so all you need to do is calculate the slope (24,319 -38,880)/2= -7280.5

Equation the is y = -7280.5x + 38880

For exponential decay need to calculate decay factor

24,319 = 38,880(r^2) r= .7909 so equation is

y= 38,880(.7909)^t

I will leave it to you to graph and analyze the equations