Mr. mole left his burrow that lies 7 meters below the ground and started digging his way deeper into the ground, descending at a

Question

2 years ago

15

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)A(t)A, left parenthesis, t, right parenthesis denote Mr. Mole's altitude relative to the ground AAA (measured in meters) as a function of time ttt (measured in minutes).
What's the functions formula?

Mathematics

2 answers:

Dimas [21] · Answer 1 · 2023-04-17T09:42:54+03:00

Answer:

$f(t)=-\frac{3}{2}t-7$

Step-by-step explanation:

We know that:

The initial conditions are -7 meters at 0 minutes.
Then, after 6 minutes, he was 16 meters below the ground.

According to these two simple facts we can found the linear function that describes this problem. First, the problem says that Mr. Mole is descending at a constant rate, which is the slope of the function. Now, to calculate the slope we need to points, which are $(0;-7)$ and $(6;-16)$ , where t-values are minutes, and y-values are meters. You can see, that the first point is the initial condition and the second point is 6 minutes later.

So, we calculate the slope:

$m=\frac{y_{2}-y_{1}}{t_{2}-t_{1}} \\m=\frac{-16-(-7)}{6-0}=\frac{-16+7}{6}=\frac{-9}{6}=\frac{-3}{2}$

From the slope we can see that Mr. Mole is descending, because it has a negative sign. Also, the point $(0;-7)$ is on the y-axis, because t is null, so -7 is part of the function. Therefore the function that describes this problem is:

$f(t)=-\frac{3}{2}t-7$