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CalculusQ&A LibraryThe normal healing of wounds can be modeled by an exponential function. If A0 represents the original area of the wound, and if A equals the area of the wound, the the function A(n)=A0e-0.35n describes the area of a wound after n days following an injury when no infection is present to retard the healing. Suppose that a wound initially had an area of 100 sqaure millimeters.a) If healing is taking place, after how many days will the wound be one-half of its original size?b) How long before the wound is 10% of its original size?Question

Asked Mar 11, 2020

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The normal healing of wounds can be modeled by an exponential function. If A_{0} represents the original area of the wound, and if A equals the area of the wound, the the function A(n)=A_{0}e^{-0.35n} describes the area of a wound after n days following an injury when no infection is present to retard the healing. Suppose that a wound initially had an area of 100 sqaure millimeters.

a) If healing is taking place, after how many days will the wound be one-half of its original size?

b) How long before the wound is 10% of its original size?

Step 1

Given that the function is:

where A_{0} is the original area of the wound and A(*n*) is the area of the wound after *n* days.

Step 2

(a) When area is one half of its original size, take:

So,

A0, will cancel out from both the sides, we get:

Taking natural logarithm on both sides, we get:

Hence, the wound becomes one-half of its original size approximately after 2 days.

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