Question

This one is about rate of change and has 2 questions that need two answers.

At 6:00 am, there was 1 inch of snow on the ground. By 11 am, there were 4 inches of snow on the ground. What is the average rate of change?

If the snow continues to fall at the same rate, how much snow will be on the ground by 1:00 pm.​

Answer 1

0.6 inches per hours

5.2 inches on the ground by 1:00 pm

Explanation:

Let x = number of hours after midnight

Let y = height of snow (in inches)

Information presented as ordered pairs (x, y):

(6, 1)

(11, 4)

`\mathsf{rate \ of \ change=(change \ in \ y)/(change \ in \ x)=(4-1)/(11-6)=\frac35 \ inches \ per \ hour}`

Written as a linear equation:

`y-1=\frac35(x-6)`

`\implies y=\frac35x-(13)/(5)`

1:00 pm = 13 hours after midnight

Therefore, when x = 13:

`\implies y=\frac35(13)-(13)/(5)`

`\implies y=5.2 \textsf{ inches}`