Chapter 2.3, Problem 14E

Decay of Radioactivity A large cloud of radioactive debris form a nuclear explosion has floated over the Pacific North-west, contaminating much of the hay supply. Consequently, farmers in the area are concerned that the cows who eat this hay will give contaminated milk. (The tolerance level for radioactive iodine in milk is $0$.). The present in the hay after $t$ days is approximated by $P\left(t\right)$, which is given by the mathematical model

$P\left(t\right)=100e^{-0.1t}$

1. Find the percent remaining after $4$ days.
2. Find the percent remaining after $10$ days.
3. Some Scientists feel that the hay is safe after the percent of radioactive iodine has declined to $10\%$ of the original amount. Solve the equation $10=100e^{-0.1t}$ to find the number of days before the hay may be used.
4. Other scientists believe that the hay is not safe until the level of radioactive iodine has declined to only $1\%$ of the original level. Find the number of days that this would take.