The value of a small airplane depreciates exponentially every year after it is purchased. The value, in thousands of dollars, alt), of Plane X, t years after purchase
can be approximated by this function.
a(t) = 131.5(0.8)
Part A
What does the number 131.5 in the function above represent in the context of the
situation?
Part B
Plane B also depreciates exponentially but at a different rate than Plane X. The table
below shows the value of Plane Y one month after it was purchased and the monthly
rate at which it is depreciating.
Time
Value of Plane Y Monthly Depreciation Rate
1 month after purchase $177,223 2.4%
Express the value of Plane Y as an exponential function similar to the one given for
the value of Plane X above, except the time will be m months after purchase. (Use
b(m) for the value of Plane Y in thousands of dollars). Provide evidence to support
your answer
Part C
Plane X and Plane Y were each purchased in the same year. Rewrite the function
from Part B so that the function, b(t), represents the value of the planet years after
it was purchased. Provide evidence to support your answer