1. ## Help with a Business Calculus problem, please- f(x)=20 - 15e^(0.2x)

When professors select texts for their courses, they usually choose from among the books already on their shelves. For this reason, most publishers send complimentary copies of new texts to professors teaching related courses. The mathematics editor at a major publishing house estimates that if x thousand complimentary copies are distributed, the first-year sales of a certain new mathematics text will be approximately f(x)=20 - 15e^(0.2x) thousand copies.

a. Assuming the editor is correct what is the most they can expect in sales?

b. How many copies can the editor expect to sell in the first year if no complimentary copies are sent out?

c. If the editor's estimate is correct, what is the most optimistic projection for the first year sales of the text?

2. ## Re: Help with a Business Calculus problem, please- f(x)=20 - 15e^(0.2x)

I would like to go with you through this problem, but not before you would show what you have tried to do by yourself

dokrbb

3. ## Re: Help with a Business Calculus problem, please- f(x)=20 - 15e^(0.2x)

Thank you- I honestly have no clue where to start, I am an online student and trying to teach myself. My book reads like another language. If I knew even the steps I would definitely attempt it.

4. ## Re: Help with a Business Calculus problem, please- f(x)=20 - 15e^(0.2x)

Originally Posted by CeisMomma
When professors select texts for their courses, they usually choose from among the books already on their shelves. For this reason, most publishers send complimentary copies of new texts to professors teaching related courses. The mathematics editor at a major publishing house estimates that if x thousand complimentary copies are distributed, the first-year sales of a certain new mathematics text will be approximately f(x)=20 - 15e^(0.2x) thousand copies.

a. Assuming the editor is correct what is the most they can expect in sales?

b. How many copies can the editor expect to sell in the first year if no complimentary copies are sent out?

c. If the editor's estimate is correct, what is the most optimistic projection for the first year sales of the text?
It's an optimization problem:
we are given 1) f(x)=20 - 15e^(0.2x) - first year sales if x thousand copies are sent out

a. asks you what is the maximum they can sales - for that we take the first derivative of f(x)=20 - 15e^(0.2x)

f'(x) = -15*(0.2)e^(0.2x) = -3e^(0.2x), set -3e^(0.2x) = 0 and solve for x, finding the critical number you would be able to find the maximum of sales by plugging the values into the original formula f(x),

what's next?