Question

A rocket is 1 mile above the earth in 30 seconds and 5 miles above the earth in 150 seconds. What is the rockets rate of change in miles per second?

Answer 1

Given:

At 30 seconds, the distance between the rocket and the earth is 1 mile.

At 150 seconds, the distance between the rocket and the earth is 5 miles.

In the points, (30,1) and (150,5)

To find:

We need to find the rate of change in miles per second.

Explanation:

$\text{Rate of change =}\frac{y_2-y_1}{x_2-x_1}$$\text{Substitute }y_2=5,y_1=1,x_2=150,\text{ and }x_1=30\text{ in the eqaution.}$

$\text{Rate of change =}\frac{5-1}{150-30}\text{ miles per second}$

$\text{Rate of change =}\frac{4}{120}\text{ miles per second}$

$\text{Rate of change =}0.033\text{ miles per second}$

Final answer:

The rocket's rate of change is 0.033 miles per second.