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(t) denote Mr. Mole's altitude relative to the ground A (measured in meters) as a function of time "t" (measured in minutes).
Write the function's formula.

Where "m" is the rate at which he descends. Note that since the function A(t) measures his altitude relative to the ground, the rate "m" must be negative (m=-1.8).

[tex]A(t) = -1.8*t + c[/tex]

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

[tex]-13.5 = -1.8*5 + c[/tex]

[tex]c = -4.5 m[/tex]

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

[tex]A(t) = -1.8t -4.5[/tex]

ajeigbeibraheem ajeigbeibraheem · Answer 2 · 2022-02-21T14:33:41+01:00

The formula for the function is A(t) = -1.8t - 4.5

To solve this question, we need to understand the concept of a linear model

What is the linear model of a general equation?

The linear model of the general equation explains the relationship among two variables for making a decision if that relationship between them is statistically relevant and significant.

From the given information, we can say that the digging carried out by Mr. Mole can be expressed by using the linear relation:

A(t) = yt + c

here:

y = the rate at which Mr. Mole descends and;
y = negative
c = constant
t = time

This is due to the position of the digging relative to the ground surface.

A(t) = -1.8t + c

After 5 minutes(time t), he was 13.5 meters below the ground.

i.e.

13.5 = -1.8(5) + c

13.5 = -9 + c

c = 13.5 - 9

c = 4.5

Therefore, we can conclude that the function of the formula after 5 minutes is:

A(t) = -1.8t - 4.5

Learn more about the Linear model here:

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