cjohn19
Answered

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?

Verified 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 

raphealnwobi

It would take 26 days for 75% of the wound to be healed

Exponential function

An exponential function is in the form:

\(y=ab^x\)

Where a is the initial value of y and b is the multiplier factor

A(t) is the area of the wound in square centimeters after t days of healing.

Given that:

\(A(t)=80(10)^{-0.023t\)

For 75% of the wound be healed, the remaining area would be 25% (100% - 75%). Hence:

  • A(t) = 25% of 80 cm² = 0.25 * 80 = 20 cm²

Hence:

\(20=80(10)^{-0.023t}\\\\\\t=26\)

It would take 26 days for 75% of the wound to be healed

Find out more on exponential function at: https://brainly.com/question/12940982