Math Calculus Question

Question

When a person stubs their toe the amount of pain they feel t minutes after the incident follows the equation S(t) = 3t + 1/ t^2 .

(a) What is the domain of this function?

(b) Does the domain make practical sense, why or why not?

Answer 1

T can be positive real..

T=2.5 means 2.5 minutes or 2 minutes and 30 seconds.

What does NOT make sense is the function.

As T approaches infinity, the amount of pain felt should go to zero.

But the way the function is written, it does not !! 3t tends to infinity while 1/t^2 vanishes.

I bet you should have written the function as

(3t+1)/t^2

THAT function vanishes as t goes to infinity.

Please use parenthesis to clarify which parts of the formula are in the numerator

and which ones are in the denominator.