Question

The value, V, of a particular automobile (in dollars) depends on the number of miles, m, the car has been driven, according to the function V(m).

A. Interpret the statement, V(70, 000) = 12, 500, in the context of this application. Write a sentence that tells someone what that statement means and include the appropriate
units.

B. In the statement f '(70, 000) = − 15

i. What are the units of the 70, 000?

ii. What are the units of the − 15?

iii. Interpret the statement, f '(60, 000) = − 15, in the context of this application.
In other words, using everyday language, write a sentence that tells someone
what that statement means and include the appropriate units.

Answer 1

A. The statement V(70,000) = 12,500 means that the value of the automobile when it has been driven for 70,000 miles is $12,500.

B.

i. The units of 70,000 are miles, since it represents the number of miles the car has been driven.

ii. The units of -15 are dollars per mile, since it represents the rate of change of the value of the car with respect to the number of miles driven.

iii. The statement f'(60,000) = -15 means that when the car has been driven for 60,000 miles, the rate of change of its value is -$15 per mile. In other words, for every additional mile the car is driven after 60,000 miles, its value decreases by $15.