Writing Equations to Represent Exponential Decay

5.5.5 Writing Equations to Represent Exponential Decay

5.5.5 • Writing Equations to Represent Exponential Decay

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Acetaminophen is a common pain reliever and fever reducer. Here is a graph showing the amount of acetaminophen, in milligrams, in an adult’s body at different times after they take a normal dose.

A graph showing acetaminophen levels (mg) decreasing over 8 hours; starting at 1000 mg at 0 hours, dropping to 750 mg at 1 hour, 562.5 mg at 2 hours, and continuing downward.

Answer the following questions.

a. What is the vertical intercept?

b. What does it mean in this situation?

Compare your answer:

a. 1,000

b. There are 1,000 mg of acetaminophen in the person’s body after taking the medicine (this is the dose size).

What fraction of the medicine remained after one hour?

Compare your answer:

$\frac{3}{4}$ of the medicine remained after 1 hour since $\frac{750}{1000} = \frac{3}{4}$ .

Write an equation that represents the amount of medicine, $a$ , after $t$ hours.

Compare your answer:

$a = 1, 000 (\frac{3}{4})^{t}$