festasphestld 177072345&icenterwin-yes; Spring 2018 UI MATH1380A15 Quiz: Chapter

Question

festasphestld 177072345&icenterwin-yes; Spring 2018 UI MATH1380A15 Quiz: Chapter 6 Review Quiz This Question: 1 pt 5000 The product current The demand function for a certain product is determined by the fact that the product of the price and the quantity demanded equals the rate of change of demand over time. Find the demand function represented in this problem where p is the price of the product and q is the quantiay demanded for the product Type an equation.) Demand is (Round to the nearest integer as needed.) at a rate of approsximately units per unit of time Enter your answer in each of the answer boxes Save for Later

Explanation / Answer

price * quantity demanded = 5000

pq = 5000

Price of each unit currently at t = 0 is : $2.40

dC/dt = 12% of C
dC/dt = 0.12C

dp/dt = 0.12*p
Solving by variable separable,
ln(p) = 0.12t + C
p = Ce^(0.12t)
p = 2.40*e^(0.12t) ---> expression for price

Demand = 5000/price

Demand = 5000/pi

So,
demand = 5000 / (2.40 * e^(0.12t))

demand = (6250/3)e^(-0.12t) ------> FIRST ANS

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Deriving :
dD/dt = 6250/3 * -0.12 e^(-0.12t)

dD/dt = -250e^(-0.12t)

So, clearly demanding is DECREASING
at the rate of 250e^(-0.12t) ----> ANS

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