Question

Mr. Mole left his burrow that lies below the ground and started digging his way deeper into the ground,

descending at a rate of 1.8 meters per minute. After 5 minutes, he was 13.5 meters below the ground.
Let A represent Mr. Mole's altitude (in meters) relative to the ground after t minutes.
Complete the equation for the relationship between the altitude and number of minutes.

Answer 1

A(t) = -1.8t - 4.5

Explanation:

Let the starting level of Mr. Mole is 'b'.

Since Mr. Mole is descending with respect to the ground, at the rate = 1.8 meters per minute

After time 't' altitude of Mr. Mole will be = b - 1.8t

If we represent the altitude of Mr. Mole with A(t).

Then the equation will be,

A(t) = b - 1.8t

Or, A(t) = -1.8t + b

At the time t = 5 minutes, his altitude was 13.5 meters.

So, -13.5 = -1.8×(5) + b

b = -13.5 + 9

b = -4.5

Now we substitute the value of b in the equation.

A(t) = -1.8t - 4.5