Question

iodine-131 is a radioactive material that decays according to the function A(t)= 100e^(-0.087t)where A(t) is the amount present in the gram at time t in dyas. 1.how much iodine is left after 9 days?(round to the nearest whole gram) 2 when will 70g of iodine be left?( round to the nearest whole day)

Answer 1

`A(t)=100\cdot e^(-0.087t)`

1. Replacing with t = 9 into the equation, we get:

`\begin{gathered} A(t)=100\cdot e^(-0.087\cdot9) \\ A(t)=100\cdot e^(-0.783) \\ A(t)=100\cdot0.457 \\ A(t)=45.7 \end{gathered}`

There are 45.7 grams of iodine left, after 9 days

2. Replacing with A(t) = 70 into the equation, we get:

`\begin{gathered} 70=100\cdot e^(-0.087t) \\ (70)/(100)=e^(-0.087t) \\ \ln ((70)/(100))=-0.087\cdot t \\ (-0.356)/(-0.087)=t \\ 4\approx t \end{gathered}`

70g of iodine will be left after 4 days