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Question

The number of Medicare-certified home-health-care agencies (70% are freestanding, certified home-health-care agencies (70% are freestanding, been declining at the rate of $0.186 e^{-0.02 t}$ $0.186 e^{-0.02 t}$ thousand agencies/year between 1988 (t = 0) and 2002 (t = 14). The number of such agencies stood at 9.3 thousand in 1988. Find an expression giving the number of health-care agencies in year t.

Solution

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Answered 1 year ago

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1 of 7To find the expression that gives the number of health-care agencies in year $t$ we will solve the following initial value problem

$\begin{array}{cccc} y^\prime(t) & = &- 0.186 & e^{-0.02t}\\ y(0) & = & 9.3 \end{array}\Bigg\}$

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