The 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?

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Asked Mar 11, 2020
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The 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?

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Expert Answer

Step 1

Given that the function is:

Calculus homework question answer, step 1, image 1

where A0 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:

Calculus homework question answer, step 2, image 1

So,

Calculus homework question answer, step 2, image 2

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

Calculus homework question answer, step 2, image 3

Taking natural logarithm on both sides, we get:

Calculus homework question answer, step 2, image 4

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

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