# Exponential Tricky Problem Solving Task

• May 7th 2012, 03:28 AM
k31453
Hi i have got this question but i cant do part c can anybody help with my question i attached the 2 photos ::::

Attachment 23803Attachment 23804
• May 7th 2012, 07:10 AM
emakarov
Re: Exponential Tricky Problem Solving Task
I assume the equation is \$\displaystyle x = At^be^{-ct}\$. Using the derivative, express the maximum point (which is t = 30) through b and c. This gives you one equation. For the second equation, you can take x(4t) = x(t) / 2 where t = 30. After some cancellations, this gives you another linear equation on b and c. From these two equations you can find b and c. Then find A from x(30) = 0.2.

The answer is below (for checking only).
Spoiler:
A = 0.071301182
b = 0.429537559
c = 0.014317919
• May 7th 2012, 04:30 PM
k31453
Re: Exponential Tricky Problem Solving Task
Quote:

Originally Posted by emakarov
I assume the equation is \$\displaystyle x = At^be^{-ct}\$. Using the derivative, express the maximum point (which is t = 30) through b and c. This gives you one equation. For the second equation, you can take x(4t) = x(t) / 2 where t = 30. After some cancellations, this gives you another linear equation on b and c. From these two equations you can find b and c. Then find A from x(30) = 0.2.

The answer is below (for checking only).
Spoiler:
A = 0.071301182
b = 0.429537559
c = 0.014317919

I dont get it can you be specify and PM me
• May 7th 2012, 04:33 PM
emakarov
Re: Exponential Tricky Problem Solving Task
Which exactly recommendation don't you get?
• May 7th 2012, 07:32 PM
k31453
Re: Exponential Tricky Problem Solving Task
The methodsbof getting answer u cant use derevitive u have to use exponential or log rules to do part c thats what teacher said
• May 8th 2012, 06:43 AM
emakarov
Re: Exponential Tricky Problem Solving Task
If you can't use derivatives, you can assume that the maximum of \$\displaystyle At^be^{-ct}\$ occurs at t = b / c. Draw several graphs for various values of b and c and verify that this is the case. The rest of the recommendations in post #2 should still work.