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

Answer:

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

(b) $\triangle = 2.22 * 10^{-4}$

Step-by-step 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:

$\triangle = \frac{f(s)}{s}$

Substitute 90 for s

$\triangle = \frac{f(90)}{90}$

Given that: $f(90) = 0.02$

$\triangle = \frac{0.02}{90}$

$\triangle = 0.000222$

$\triangle = 2.22 * 10^{-4}$