Lesson 2

In Try This 2 you looked at solving exponential equations algebraically by writing each side of the equation with equivalent exponents that had the same base. In Try This 3 you will explore how to solve exponential equations graphically.

Try This 3

The medical isotope iodine-131 is produced at Chalk River Laboratories in Ontario and is used in imaging and diagnosing thyroid problems. A radioactive sample of iodine-131 has a half-life of 8 days. This means that after 8 days, half of the original amount of the sample has decayed.

The equation that can be used to describe the half-life function is

where A is the remaining mass of iodine-131, A0 is the original mass of iodine-131, and t is the time in days.

1. Notice that in the function, the value of parameter b is . Can you determine if this is exponential growth or exponential decay? Explain your reasoning.
2. How long would it take a 4.0-g sample of iodine-131 to decay to 0.25 g?
   1. Determine the time algebraically.
   2. Determine the time using a graph. Describe the process you used.

Save your responses in your course folder.