A van is purchased new for $29,200 . a. Write a linear function of the form y = m t + b to represent the value y of the vehicle t years after purchase. Assume that the vehicle is depreciated by $2920 per year. b. Suppose that the vehicle is depreciated so that it holds only 80 % of its value from the previous year. Write an exponential function of the form y = V 0 b t , where V 0 is the initial value and t is the number of years after purchase. c. To the nearest dollar, determine the value of the vehicle after 5 yr and after 10 yr using the linear model. d. To the nearest dollar, determine the value of the vehicle after 5 yr and after 10 yr using the exponential model.
A van is purchased new for $29,200 . a. Write a linear function of the form y = m t + b to represent the value y of the vehicle t years after purchase. Assume that the vehicle is depreciated by $2920 per year. b. Suppose that the vehicle is depreciated so that it holds only 80 % of its value from the previous year. Write an exponential function of the form y = V 0 b t , where V 0 is the initial value and t is the number of years after purchase. c. To the nearest dollar, determine the value of the vehicle after 5 yr and after 10 yr using the linear model. d. To the nearest dollar, determine the value of the vehicle after 5 yr and after 10 yr using the exponential model.
Solution Summary: The author explains the linear function of the form y=mt+b and the exponential function.
a. Write a linear function of the form
y
=
m
t
+
b
to represent the value y of the vehicle t years after purchase. Assume that the vehicle is depreciated by
$2920
per year.
b. Suppose that the vehicle is depreciated so that it holds only
80
%
of its value from the previous year. Write an exponential function of the form
y
=
V
0
b
t
,
where
V
0
is the initial value and t is the number of years after purchase.
c. To the nearest dollar, determine the value of the vehicle after 5 yr and after 10 yr using the linear model.
d. To the nearest dollar, determine the value of the vehicle after 5 yr and after 10 yr using the exponential model.
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