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(t) denote Mr. Mole's altitude relative to the ground A (measured in meters) as a function of time t (measured in minutes).

Write the function's formula.
A(t)=

Answer 1

The formula is: -1.5(t)

Answer 2

The function's formula is
`A(t)=-1.5t-7`.

Explanation:

It is given that Mr. Mole left his burrow that lies 7 meters below the ground and after 6 minutes, he was 16 meters below the ground.

It means the line passing thought the points (0,-7) and (6,-16). It means the initial value is -7.

He started digging his way deeper into the ground, descending at a constant rate. The rate of change is

`m=(y_2-y_1)/(x_2-x_1)`

`m=(-16-(-7))/(6-0)`

`m=(-16+7)/(6)`

`m=-1.5`

The rate of change is -1.5.

A(t) denote Mr. Mole's altitude relative to the ground A (measured in meters) as a function of time t (measured in minutes).

`A(t)=\text{Rate of change}* t+\text{Initial value}`

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

Therefore the function's formula is
`A(t)=-1.5t-7`, here negative sign shows the Mr. Mole's altitude relative to below the ground A.