SOLUTION: 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 would after n days, then the

Question 759722: 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 would after n days, then the formula below describes the area of a wound on the nth day following an injury when no infection is present to retard the healing.
A = A_0e^-0.36n
Suppose that a wound initially had an area of 100 square millimeters.
1.If healing is taking place, how long will it be before the wound is exactly one-half its original size?
2.How long will it be before the wound is exactly 10% of its original size?
I cant figure out how to calculate this i dont understand A_0
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
hi there,
Normally the equation would be laid out like this:
A(t) = A(o)e^-0.36t
A(t) = time after the event has taken place.
A(o) = time at the start of the event.
1) How long before wound is half its size
A(t) = A(o)e^-0.36t
50 = 100 e^-0.36t
50/100 = e^-0.36t
0.5 = e^-0.36t
Take loge of both sides.
-0.36t comes in front
loge 0.5 = -0.36t loge e (loge e = 1)
loge 0.5 = -0.36t
loge 0.5/-0.36 = t
t = 1.9 or 2 days.
2) 10% of its original size
10% of 100 = 10
A(t) = A(o)e^-0.36t
10 = 100e^-0.36t
10/100 = e^-0.36t
0.1 = e^-0.36t
Take loge of both sides
-0.36t comes in front
loge 0.1 = -0.36t loge e
loge 0.1/-0.36 = t
t = 6.39days.
Hope this helps.
:-)
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