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# argh math watch

1. An economist tells you that,according to his mathmatical model, the best time to sell an antique painting is the value of t for which the function

P(t) = (1000 + 250t)e^-(0.1)t

takes the maximum value. Given this,find the best time to sell.
2. (Original post by Teatime)
An economist tells you that,according to his mathmatical model, the best time to sell an antique painting is the value of t for which the function

P(t) = (1000 + 250t)e^-(0.1)t

takes the maximum value. Given this,find the best time to sell.
Differentiate and set to equal 0, then differentiate again to find the max and min numbers, which can be substitued back in to get the value.
4. (Original post by Teatime)
What do you mean? His reply makes sense..
5. I agree but the problem is that I can't differentiate very well. So please give me a more thorough solution. Thank you in advance.
6. (Original post by Teatime)
I agree but the problem is that I can't differentiate very well. So please give me a more thorough solution. Thank you in advance.
use the chain rule.
7. According to my calculations t = 0, however it coludn't be zero since the time (t) sholud be more than zero. Please, I desperately need a solution.
8. P'(t) = -(100+25t)e^-0.1t + 250e^-0.1t = 0 for maximum

=> 250 = 100+25t

=> t = 150/25 = 6.
9. How (1000 + 250t) becomes -(100+25t) ???????? I am puzzled
10. Is it something to do with multiplying the brackets by the power outside? (-0.1)?
11. (Original post by GeneralGrievous)
use the chain rule.
Surely you mean the product rule?
12. If P(t) = (1000 + 250t)e^-(0.1)t then both the product rule and the chain rule need to be used.

You need to use (1000 + 250t) and e^-(0.1)t as your individual products. The derivative of (1000 +250t) is 250 and the derivative of e^-(0.1)t is -(0.1)e^-(0.1)t.

So, you should get 250*e^-0.1t+-0.1e^-0.1t*(1000+250t)

Simplifying:250e^-0.1t - 0.1(1000+250t)e^-0.1t
250e^-0.1t - (100+25t)e^-0.1t
Factorising: 25e^-0.1t(10-4-t)
Simplifying even more: (25e^(-0.1t))(6-t)

when that's equal to zero t=6 as the dude said so you have one place where the gradient is equal to zero. you can hope that it's a maximum cos that's what you want (if I remember reading the question correctly) or alternatively you can check it by calculating the value when t is 5 and when t is 7.
13. (Original post by Nylex)
Surely you mean the product rule?
the product rule is a direct derivative of the chain rule. (and by derivative i do not mean analytical derivative).
14. (Original post by Teatime)
How (1000 + 250t) becomes -(100+25t) ???????? I am puzzled
(1000 + 250t)*(-0.1) = -(100+25t)

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