calculus II exponential growth and decay

Question

1a) Give an example of a differential equation that models exponential decay.

b) Describe a scenario that could be modeled by your differential equation. Be sure that your description references the relationship between the quantity and its rate of change.

Answer 1

I will be giving you an example of exponential growth, so you can find an example of exponential decay by yourself.

"The concentration C of a certain drug in a patient's bloodstream t minutes after injection is given by C(t)=50t/t^2+25"

C(t) is the measure or amount of the drug in the patient's bloodstream at t minutes.

dC/dt is the rate at which the drug enters the patient's bloodstream.

This can be placed in the scenario of a hospital and injections, connecting the quantity of the drug bloodstream to the rate of change at which the drug enters the patient's bloodstream.

Cheers!