Question

The area of a wound decreases exponentially with time. The area A of a wound after t days can be modeled by A= A₀e⁰.⁰⁵ᵗ where A₀ is the initial wound area. If the initial wound area is 4 square centimeters, a. What is the wound area after 14 days? b. When will the area of the wound becomes one fourth its initial size?

a) 2.5 cm² b) At: 30.57 days
a) 1.99 cm² b) At: 27.7 days
a) 0.5 cm² b) At: 17.7 days

Answer 1

The wound area after 14 days is approximately 2.5 cm². The area of the wound becomes one fourth its initial size at approximately 30.57 days.

Step-by-step explanation:

To find the wound area after 14 days, we can substitute t = 14 into the equation A = A₀e^(0.05t). Given that A₀ = 4 square centimeters, we have A = 4e^(0.05 * 14). Using a calculator, the wound area after 14 days is approximately 2.5 cm².

To find when the wound area becomes one fourth its initial size, we need to solve the equation A = A₀e^(0.05t) for t. We want A = A₀/4, so we have A₀e^(0.05t) = A₀/4. Dividing both sides by A₀ gives e^(0.05t) = 1/4. Taking the natural logarithm of both sides gives 0.05t = ln(1/4). Solving for t, we get t = ln(1/4) / 0.05. Using a calculator, we find that t is approximately 30.57 days.