Answer:
[tex]A(t)=-1.5t-7[/tex]
Step-by-step 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=[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{-16+7}{6-0}=\frac{-9}{6}=-1.5[/tex]
Rate of change=-1.5 m/s
The negative sign shows that rate of change decreases.
Therefore, the function
[tex]A(t)=Rate of change\times time+initial value[/tex]
Substitute the values
Then, the function
[tex]A(t)=-1.5t-7=-(1.5t+7)[/tex]
Here, negative shows that the altitude decreases with time.
