anonymous
  • anonymous
When toasters are sold for p dollars a piece, local consumers will buy D(p)=57,600/p toasters a month. It is estimated that t months from now,the price of the toasters will be p(t)=0.03t^3/2 + 22.08 dollars. Compute the rate at which the monthly demand for the toasters will be changing with respect to time 16 months from now. I get -75.47, it will decrease. Is that correct?
Mathematics
chestercat
  • chestercat
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amistre64
  • amistre64
I get dD/dt = dD/dp * dp/dt -57600/(24^2) * .03(3/2)(4) I get it at: -18. Demand is dropping at a rate of 18 units at 16 months. But I could be wrong :)
anonymous
  • anonymous
where do you get 24^2
amistre64
  • amistre64
p(16) = .03 (sqrt(16^3)) + 22.08 .03(16*4) + 22.08 .03(64) + 22.08 1.92 + 22.08 = $24.00 at 16 months

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amistre64
  • amistre64
dD/dp = -57600/p^2; p=24 at 16 months.
anonymous
  • anonymous
for the 57600/p^2 p=24 at 16 months shouldn't that be the derivative of 57699/p which I think would be -115200p^-2?
amistre64
  • amistre64
Quotient rule: top: (BT')-(B'T) bottom: B^2 T=57600; T' = 0 B=p ; B'=1 top: (p*0) - (1*57600) bottom: p^2 The change in demand (D) with respect to price (p): (dD/dp) = -57600/p^2

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