Casey recently purchased a sedan and a pickup truck at about the same time for a new business. The value of the sedan S
, in dollars, as a function of the number of years t
after the purchase can be represented by the equation S(t)=24,400(0.82)t
. The equation P(t)=35,900(0.71)t2
represents the value of the pickup truck P
, in dollars, t
years after the purchase. Analyze the functions S(t)
and P(t)
to interpret the parameters of each function, including the coefficient and the base. Then use the interpretations to make a comparison on how the value of the sedan and the value of the pickup truck change over time.(4 points)
The parameter 0.82 in the function S(t)=24,400(0.82)^t represents the base of the exponential function, which determines how the value of the sedan changes over time. In this case, the base 0.82 indicates that the value of the sedan decreases by 18% every year. The coefficient 24,400 represents the initial value of the sedan.
On the other hand, the parameter 0.71 in the function P(t)=35,900(0.71)^t represents the base of the exponential function for the pickup truck, which determines how the value of the pickup truck changes over time. The base 0.71 indicates that the value of the pickup truck decreases by 29% every year. The coefficient 35,900 represents the initial value of the pickup truck.
Comparing the two functions, we can see that the value of the pickup truck decreases at a faster rate than the value of the sedan over time. This means that the pickup truck loses its value more quickly compared to the sedan. This could be due to factors such as depreciation rate, maintenance costs, and market demand for each type of vehicle.