Question

Researchers at a major car company have found a function that relates gasoline consumption to speed for a particular model of car. In particular, they have determined that the consumption, C, in liters per kilometer, at a given speed, s. is given by a function C = f(s), where s is the car's speed in kilometers per hour.

Required:
a. What are the units on f'(s)?
b. Data provided by the car company tells us that f(80) = 0.015, f(90) = 0.02, and f(100) = 0.027. Use this information to estimate the instantaneous rate of change of fuel consumption with respect to speed at s = 90

Answer 1

(a) The units of f'(s) is kilometer per liter

(b)
`\triangle = 2.22 * 10^(-4)`

Explanation:

Given

`C = f(s)`

`f(80) = 0.015, f(90) = 0.02, f(100) = 0.027`

Solving (a): Unit of f'(s)

From the question, we understand that:

`C = f(s)`

and

`C = Litre/km` --- units

f'(s) is the inverse of C.

Hence:

i.e.

`f'(s) = C^(-1)` --- units

So, we have:

`f'(s) = (Litre/km)^(-1)`

`f'(s) = Km/Litre`

Solving (b): Instantaneous rate of change at:

`s = 90`

We have:

`C = f(s)`

The change is calculated as:

`\triangle = (f(s))/(s)`

Substitute 90 for s

`\triangle = (f(90))/(90)`

Given that:
`f(90) = 0.02`

`\triangle = (0.02)/(90)`

`\triangle = 0.000222`

`\triangle = 2.22 * 10^(-4)`