Chapter 8.2, Problem 32ES

Methylmercury is a toxic compound that can lead to neurological problems and an increased risk of heart disease. It takes about 50 days for the human body to eliminate $50\%$ of a given quantity of the compound from the system. Suppose a test shows that there are 600 micrograms of methylmercury in a person’s body and that $y\left(t\right)$ is the number of micrograms present t days later. Assume that $y\left(t\right)$ has as an exponential decay model with a half-life of 50 days and that no additional methylmercury is absorbed from the environment.

(a) Find an initial-value problem whose solution is $y\left(t\right).$

(b) Find a formula for $y\left(t\right).$

(c) How many milligrams will be present after 4 weeks?

(d) How long will it take for $70\%$ of the methylmercury to be eliminated from the person’s body?