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A wound, initially with an area of 80 cm^2, heals according to the formula A(t) = 80(10^-0.023t), where A(t) is the area of the wound in square centimetres after t days of healing. In how many days will 75% of the wound be healed?

Answers

Answer 1
Answer: When we have a 75% of the wound healed, we have the following area:
area of the wound=(100%-75%) (initial area) =25% (initial area)
In this case:
area of the wound=25%(80 cm²)=20 cm²

A(t)=80(10^-0.023t)
If A(t)=20
Then:
20=80(10^-0.023t)
10^-0.023t=20/80
10^-0.023t=0.25
log (10^-0.023t)=log 0.25
-0.023t log 10=log0.25          log 10=1
-0.023t=log0.25
t=log 0.25 /-0.023
t=26.176≈26

The wound be healed (75%) in 26 days 
Answer 2
Answer:

Final answer:

To find out when 75% of the wound will be healed, you need to solve the equation 80(10^-0.023t) = 0.25 * 80 for t. The solution of this equation provides the expected number of days for 75% wound healing, given the mathematical model of the healing process represented by the formula. The healing process involves several stages such as clotting, scab formation and angiogenesis.

Explanation:

To determine when 75% of the wound will be healed, you need to find the time t when the area of the wound is 25% of the original area (because 100% - 75% = 25%). According to the formula A(t) = 80(10^-0.023t), the original area is 80 cm^2.

Therefore, you want to solve the equation 80(10^-0.023t) = 0.25 * 80, which simplifies to 10^-0.023t = 0.25. Converting both sides to logarithms, you get -0.023t log(10) = log(0.25). As log(10) equals to 1, you are left with -0.023t = log(0.25). Dividing both sides by -0.023 results in t = log(0.25) / -0.023.

Calculating the value on the right side of this equation will give you the number of days needed for 75% of the wound to heal. This wound healing process involves several stages of tissue repair, including clotting, scab formation, fibroblast activity, angiogenesis, and wound contraction. The rate of healing as given by the provided formula may reflect the efficiency of these processes varying over time.

Learn more about wound healing here:

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