Question

A pharmaceutical company is testing two treatments, A and B, that are used to heal wounds.

They test the effectiveness of treatment A by applying it on an area of a 1 square inch wound. It heals by decreasing the area of the wound at a rate of 5.5% per day.

They then test the effectiveness of treatment B by applying it on an area of a 2 square inch wound. It heals by decreasing the area of the wound at a rate of 12.4% per day.

The equation below can be used to determine the number of days, x, it will take for the area of the wounds to be equal

Rounded to the nearest day, approximately how long will it be for the area of the wounds to be equal?

e-0.055x=2e-0.124x

Answer 1

From the equation e^(-0.055x) = 2e^(-0.124x), we can first take the natural logarithm of both sides:
ln(e^(-0.055x)) = ln(2e^(-0.124x))
ln(e^(-0.055x)) = ln2+ln(e^(-0.124x))
Since ln(e^a) = a,
-0.055x = ln2 - 0.124x
0.069x = ln2
x = 10.05, or approximately 10 days