Mathematics, 25.07.2019 18:40 ridjebeberjejej7502

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?

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Answer from: jose55221

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

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:

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

Answer from: bella2284

The function formula describes the situation is $f(t)=\frac{-3}{2}t-7$ .

Step-by-step explanation:

Given: 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.

According to question,

Intially Mr. mole is at meters below the ground at minutes

and he was meters below the ground at minutes.

Mr. mole is digging and descending at a constant rate which form a linear function.

Therefore, the intial position of Mr. mole is A(0, -7) and final position is B(6, 16) .

Slope of line whose points are $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is given by $\frac{y_{2}-y_{1}}{x_2-x_1}.$

$\begin{aligned}\rm{Slope\;of\;the\;line\;AB}&=\dfrac{-16-(-7)}{6-0}\\&=\dfrac{-9}{6}\\&=\dfrac{-3}{2} \end{aligned}$

Now, the point is on the axis, because is null, so is part of the function.

Linear function describes the situation is $f(t)=\frac{-3}{2}t-7$

Hence, the function formula is $f(t)=\frac{-3}{2}t-7$ .

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