# Minimum Price?

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• Apr 14th 2010, 05:08 PM
akuczma86
Minimum Price?
The price P of a certain computer system decreases immediately after its introduction and then increases. If the price P is estimated by the formula $P = 160t^2 - 1700t + 6700$, where t is the time in months from its introduction, find the time until the minimum price is reached.

First derivative of P = $320t - 1700 = 0.$
$320t = 1700.$
$t = 5.3125.$

$160(5.3125)^2 - 1700(5.3125) + 6700 = 2184.375$

I've made it this far, but how do I solve for the minimum price?
• Apr 14th 2010, 05:10 PM
Prove It
Quote:

Originally Posted by akuczma86
The price P of a certain computer system decreases immediately after its introduction and then increases. If the price P is estimated by the formula $P = 160t^2 - 1700t + 6700$, where t is the time in months from its introduction, find the time until the minimum price is reached.

First derivative of P = $320t - 1700 = 0.$
$320t = 1700.$
$t = 5.3125.$

$160(5.3125)^2 - 1700(5.3125) + 6700 = 2184.375$

I've made it this far, but how do I solve for the minimum price?

Didn't you just do that?
• Apr 14th 2010, 05:12 PM
Suhada
You've solved it already!
Time untill until minimum price is 5.3125
Minimum price is 2184.375
• Apr 14th 2010, 05:17 PM
akuczma86
lol This is why I come here to check. Thanks!