Question

The fuel consumption of a car, in miles per gallon (mpg), is modeled by f(s) = ge where s is the speed of the car, in miles per hour. if the car is traveling at 50 miles per hour and its speed is changing at the rate of 20 miles/hour ? what is the rate at which its fuel consumption is changing?

Answer 1

To find the rate at which the fuel consumption is changing, we can use the chain rule of differentiation.

Step-by-step explanation:

The fuel consumption of the car is modeled by the function f(s) = ge, where s is the speed of the car in miles per hour (mph). We are given that the car is traveling at 50 mph and its speed is changing at a rate of 20 mph. To find the rate at which its fuel consumption is changing, we can use the chain rule of differentiation.

Let's differentiate the function f(s) = ge with respect to time t:

df/dt = df/ds * ds/dt = (ge)' * (ds/dt)

Since ds/dt is given as 20 mph, we need to find the derivative of the function ge. Differentiating with respect to s, we get:

(ge)' = g(e)' = g * e

Therefore, the rate at which the fuel consumption is changing is df/dt = (ge)' * (ds/dt) = g * e * 20 mph.