Training Camp (cont 4)

Having the ability to solve exponential equations involving decay or growth is important. Example 3 demonstrates how to solve an exponential equation that models bacterial growth.

A bacterial culture starts with 3 000 bacteria. After 3 hours, the estimated count is 48 000. The exponential growth function that represents this is where d is the doubling period, in hours, for the bacterial culture and N(t) is the number of bacteria after t hours. What is the doubling period for this bacterial culture? The doubling period for this bacterial culture is hours or 45 minutes.

In many exponential decay problems, skills with exponential equations can be used. The half-life of a substance is the length of time required for the substance to decay to half its original amount. Analysis of half-lives is very important in medical testing, archaeology, and applications involving light intensity. The next example in your textbook explores two ways to solve an exponential equation that involves half-life.

Read pages 357-359 Example 3 in your textbook, Principles of Mathematics 12. Complete Your Turn on page 359 (a) and page 363 (10a & 10b) for more practice solving exponential equations involving half-life. Click here to verify your answers.