Help with a precalculus question please
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Help with a precalculus question please

[From: ] [author: ] [Date: 12-04-04] [Hit: ]
Thanks so much for the help!-S(p)= 150e^(0.004p) =480e^(-0.003p) =D(p).You need to solve for p in the equation 150e^(0.004p) =480e^(-0.......
The supply function and the demand function for the sale of a type of DVD player are given by S(p)= 150e^(0.004p) and D(p)= 480e^(-0.003p) where S(p) is the number of DVD players that the company is willing to sell at the price p and D(p) is the quantity that the public is willing to buy at price p. Find p such that D(p)=S(p).

It's really long I know. Thanks so much for the help!

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S(p)= 150e^(0.004p) =480e^(-0.003p) =D(p).

You need to solve for p in the equation 150e^(0.004p) =480e^(-0.003p)

So take ln of both sides:
ln(150e^(0.004p)) = ln(480e^(-0.003p))

use the ln rule that ln(x*y)=lnx+lny to get

ln150+ln(e^.004p)=ln480 +ln(e^-.003p)

we know that lne^x=x, so

ln 150 +.004p = ln480+( - .003p)

Now the hard part is done, solve for p!

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150e^(0.004p) = 480e^(-0.003p)
Take ln,
ln150 + 0.007p = ln480
p = 166.164
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