Question

Mr. Mole left his burrow that lies below the ground and started digging his way at a constant rate deeper into the ground.

Let yyy represent Mr. Mole's altitude (in meters) relative to the ground after xxx minutes.
Which of the following could be the graph of the relationship?

Answer 1

`A(t)=-1.8t-4.5`

Explanation:

Mr.Mole's digging can be described by a linear model of general equation:

`A(t)=m*t+c`

Where "m" is the rate at which he descends. Note that since the function A(t) measure his altitude relative to the ground, the rate "m" must be negative.

`(m=-1.8)`

`A(t)=-1.8*t+c`

The constant "c" is his starting position. To find this value, assign the given data at t = 5 min to the equation above

`-13.5=-1.8*5+c\\c=-4.5m`

Therefore, the function A(t) is described by the following formula:

`A(t)=-1.8t-4.5`