Section B Section B Checkpoint

Problem 1

Scientists in a laboratory have a sample of a material that contains many types of atoms. One of the atoms is iodine-131, a radioactive isotope used to treat some forms of cancer. Every day, about 110\frac{1}{10} of the iodine-131 present releases some radioactive material and turns into another type of atom.

  1. Scientists measure a particular sample and find that it has 5 grams of iodine-131 in it. Write an equation for AA, the amount of the iodine-131 left tt days after it was measured.
  2. What is the value of AA when t=-1t=\text{-}1? Explain what it means in this situation.
  3. Sketch a graph that shows the general shape of this equation. Include the coordinates of the vertical intercept.

blank coordinate grid from -10 to 10 on both axes

Show Solution
Solution
  1. A=5⋅(910)tA = 5 \boldcdot \left( \frac{9}{10} \right)^t or equivalent.
  2. About 5.56 grams. Sample response: It is the amount of iodine-131 one day before the scientist measured the amount in the sample.
  3. A graph that shows exponential decay and includes the point (0,5)(0,5).
Show Sample Response
Sample Response
  1. A=5⋅(910)tA = 5 \boldcdot \left( \frac{9}{10} \right)^t or equivalent.
  2. About 5.56 grams. Sample response: It is the amount of iodine-131 one day before the scientist measured the amount in the sample.
  3. A graph that shows exponential decay and includes the point (0,5)(0,5).