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)
1. Parameters of each function:
- For the sedan's value function S(t)=24,400(0.82)t:
- The coefficient is 24,400, which represents the initial value of the sedan when t=0.
- The base is 0.82, which represents the rate at which the value of the sedan decreases over time.
- For the pickup truck's value function P(t)=35,900(0.71)t2:
- The coefficient is 35,900, which represents the initial value of the pickup truck when t=0.
- The base is 0.71, which represents the rate at which the value of the pickup truck decreases over time squared.
2. Interpretation and comparison:
- The coefficient for the pickup truck's initial value is higher than that of the sedan, indicating that the pickup truck has a higher initial value than the sedan.
- The base for the sedan is 0.82, which is smaller than the base for the pickup truck (0.71), indicating that the value of the sedan decreases at a slower rate than the value of the pickup truck over time.
- Overall, the pickup truck depreciates at a faster rate than the sedan, resulting in a quicker decrease in value over time. This suggests that the pickup truck may lose its value more rapidly compared to the sedan.