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Question

The supply $S(t)$ and demand $D(t)$ functions for a commodity are given in terms of the unit price $p(t)$ at time $t$. Assume that price changes at a rate proportional to the shortage $D(t)-S(t)$, with the indicated constant of proportionality $k$ and initial price $p_0$. In each exercise:

(a) Set up and solve a differential equation for $p(t)$.

(b) Fund the unit price of the commodity when $t=4$.

(c) Determine what happens to the price as $t \rightarrow \infty$.

$S(t)=1+p(t) ; D(t)=2+8 e^{-k / 2} ; k=0.03 ; p_0=2$

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 4We are required to:

**(A)**Generate the differential equation using the formula $D(t)-S(t)$.**(B)**Determine the unit price at $t=4$.**(C)**Determine the unit price at $t$ approaches to infinity.

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