What is the Average Value of a Function?

[olicoh]

The problem and attempted solution is in the attached document.
My teacher said:
"This is a confusing question. They use the word 'rate' in the description of the information. But, if you change 'growth rate' to 'something' they are asking for the average something, not the rate of change of something."

What does she mean? How do I need to setup the problem differently?

 

[Citan Uzuki]

Your formula gives the average for the rate of change of a function, and so what you've computed gives the average of the rate of change of the growth rate (i.e. the average of r'(t)). But you're looking for the average of the growth rate itself, i.e. the average of r(t). So you need to use the formula with the integral in it.

Also, the name of the function is r, not f, so your computations should involve the letter r, not the letter f.

 

[Char. Limit]

Your formula gives the average for the rate of change of a function, and so what you've computed gives the average of the rate of change of the growth rate (i.e. the average of r'(t)). But you're looking for the average of the growth rate itself, i.e. the average of r(t). So you need to use the formula with the integral in it.

Also, the name of the function is r, not f, so your computations should involve the letter r, not the letter f.

Unless, of course, you explicitly define r(t)=f(t).

 

[Citan Uzuki]

Unless, of course, you explicitly define r(t)=f(t).

Pedant.