5.5.7 Lesson Summary

In this lesson, you learned how to:

• Use only multiplication to represent “decreasing a quantity by a fraction of itself.”
• Write an expression or equation to represent a quantity that decays exponentially.
• Know the meanings of “exponential growth” and “exponential decay.”
• Explain the meanings of $a$ and $b$ in an equation that represents exponential decay and is written as $y=a·b^x$.
• Find a growth factor from a graph and write an equation to represent exponential decay.
• Graph equations that represent quantities that change by a growth factor between 0 and 1.

Here are the activities that helped you reach those goals:

• 5.5.1: Identifying Linear and Exponential Quantities
  • In this activity, you analyzed the difference between linear and exponential tables. You also extended the pattern of the equation of each.
• 5.5.2: Exponential Decay
  • In this activity, you learned how the value of a used car can be represented using exponential decay. You also learned how to use the values from the problem to write the equation.
  • 5.5.2: Self Check
  • 5.5.2: Additional Resources
• 5.5.3: Using Graphs to Represent Exponential Decay
  • In this activity, you analyzed how an algae bloom shrinks after being treated. The values of the equations were analyzed in the context of the situation, and each of the observations was graphed.
  • 5.5.3: Self Check
  • 5.5.3: Additional Resources
• 5.5.4: Justifying Exponential Models
  • In this activity, you analyzed how much insulin is left in a diabetic’s bloodstream over time. This scenario was used to justify the fact that the insulin decreases exponentially over time.
  • 5.5.4: Self Check
  • 5.5.4: Additional Resources
• 5.5.5: Writing Equations to Represent Exponential Decay
  • In this activity, you used the graph of the breakdown of acetaminophen to create an exponential equation to represent the situation.

After these activities, you completed the following practice :

• 5.5.6: Practice