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

Answer:

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

Step-by-step 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

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-16-(-7)}{6-0}$

$m=\frac{-16+7}{6}$

$m=-1.5$

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).

$A(t)=\text{Rate of change}\times t+\text{Initial value}$

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

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.