Question

Mr. Mole left his burrow that lies 7 meters below the ground and started digging his way deeper into the ground, descending at a constant rate. After 6 minutes, he was 16 meters below the ground. Let A represent Mr. Mole's altitude (in meters) relative to the ground after ttt minutes.

Answer 1

`A(t)=-1.5t-7`

Explanation:

We are given that

Mr. mole left his burrow that lies 7 meter below the ground .

Therefore, the coordinates of the point (0,-7).

Because initially t=0 and y=-7

After 6 minutes ,

He was 16 meters below the ground.

Therefore, the coordinates of the point (6,-16).

When A represent Mr. Mole's altitude (in m) relative to the ground after t minutes.

Then, we hate to find the function A(t).

When he started digging his way deeper into ground , at a constant rate.

Then, the rate of change=
`(y_2-y_1)/(x_2-x_1)=(-16+7)/(6-0)=(-9)/(6)=-1.5`

Rate of change=-1.5 m/s

The negative sign shows that rate of change decreases.

Therefore, the function

`A(t)=Rate of change* time+initial value`

Substitute the values

Then, the function

`A(t)=-1.5t-7=-(1.5t+7)`

Here, negative shows that the altitude decreases with time.