A delivery truck is purchased new for $54,000 . 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 $6750 per year. b. Suppose that the vehicle is depreciated so that it holds 70 % 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 4 yr and after 8 yr using the linear model. d. To the nearest dollar, determine the value of the vehicle after 4 yr and after 8 yr using the exponential model.
A delivery truck is purchased new for $54,000 . 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 $6750 per year. b. Suppose that the vehicle is depreciated so that it holds 70 % 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 4 yr and after 8 yr using the linear model. d. To the nearest dollar, determine the value of the vehicle after 4 yr and after 8 yr using the exponential model.
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
$6750
per year.
b. Suppose that the vehicle is depreciated so that it holds
70
%
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 4 yr and after 8 yr using the linear model.
d. To the nearest dollar, determine the value of the vehicle after 4 yr and after 8 yr using the exponential model.
. Determine whether a linear or an exponential function is the better fit for the data in the table. Then findthe equation of the function with three-decimal-placeaccuracy
The following table gives the monthly premiums for an insurance policy on people of various ages.
a. Find an exponential function that models the monthly
premium as a function of age.
b. Find the quadratic function that is the best fit for the data.
c. Graph each function with the data points to determine
which model is the better fit.
a. The exponential function that models the data is y= 3.059 (1.104*).
(Use integers or decimals rounded to the nearest thousandth as needed for any numbers in the expression.)
b. The quadratic function that models the data is y= 6.188x2-557.818x+12,448.185.
(Use integers or decimals rounded to the nearest thousandth as needed for any numbers in the expression.)
Age
35
40
45
50
55
Monthly
Premium (S)
127
164
242
362
559
Age
60
65
70
75
Full data set
Monthly
Premium (S)
946
1904
3485
5873
A house increases in value in a linear fashion from $220,000 to $300,000 in 5 years.Find the appreciation function that gives the value of the house in year x.If the house continues to appreciate at this rate, how much will it be worth 12 years from now?
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
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