Question

A ski resort has 18 inches of snow on the ground. The snow is falling at a rate of 4 inches per hour. which type of functions best model this situation?​

Answer 1

Linear decreasing function best model this situation and the required function is

f(x)=4x+18

Explanation:

It is given that a ski resort has 18 inches of snow on the ground. The snow is falling at a rate of 4 inches per hour.

If a function has constant rate of change, then the it is a linear function.

It the given case the rate of change is constant so linear function best model this situation.

The slope intercept form of linear function is

`f(x)=mx+b` ... (1)

where, m is slope and b is y-intercept or initial value.

Ski resort has 18 inches of snow on the ground it means initial value is 18.

The snow is falling at a rate of 4 inches per hour. So, m=4.

Substitute m=4 and b=18 in equation (1).

`f(x)=4x+18`

Therefore the required function is f(x)=4x+18.

Answer 2

Linear Function

`y=4x+18`

Explanation:

Let

x----> the time in hours

y----> the total inches of snow on the ground

we know that

The function that best model this situation is the linear function

so

`y=mx+b`

In this problem

`m=4(in)/(h)`

`b=18\ in` ----> the y-intercept

substitute

`y=4x+18`