
Concept explainers
(a)
The graph and which kind of function models the data
(a)

Answer to Problem 28PPS
The ordered pairs represent an exponential function
Explanation of Solution
Given:
Concept Used:
If first difference of y-values is equal, then model be linear
If second difference be equal, then the model be quadratic
If first and second differences are not equal then the model will be exponential
Calculation:
In order to check whether the given data is linear, quadratic or exponential, find the first difference as shown below:
First differences:d=y2−y1=15910−18500=−2590d=y3−y2=13682.60−15910=−2227.4d=y4−y3=11767.04−13682.60d=−1915.56Second differences:d=−2227.4−(−2590)d=362.6d=1915.56−2227.4d=311.84Ratio of y-values:r1=a2a1=1591018500=0.86r2=a3a2=13682.615910=0.86
Thus, the first difference of y-values is not equal but the second difference is also no equal, so the given data represents an exponential model
General equation of exponential function is given by v=abx
(b)
The equation for the function that models the data
(b)

Answer to Problem 28PPS
The equation is v=18500(0.86)t
Explanation of Solution
Given:
Concept Used:
If first difference of y-values is equal, then model be linear
If second difference be equal, then the model be quadratic
If first and second differences are not equal then the model will be exponential
Calculation:
In order to the equation the ratio is 0.86 b=0.86 a is the initial value of car a=18500
Thus, the equation is given by v=18500(0.86)t
(c)
How much the car is worth after 7 years.
(c)

Answer to Problem 28PPS
The cost is $6436.66 .
Explanation of Solution
Calculation:
In order to find the cost of car in 7 years shown below:
v=18500(0.86)tt=7v=18500(0.86)7=18500(0.3479)v=6436.66
Thus, the cost is $6436.66 .
Chapter 9 Solutions
Algebra 1
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