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It will take approximately 21.67 hours for the initial 500 mg of medicine to decrease to 40 mg.

Would you like more details on the steps? Here are some related questions:

1. How does exponential decay work in real-world situations like medicine wearing off?
2. Can the decay rate of 0.89 be interpreted in terms of percentage?
3. How do we solve logarithmic equations in exponential decay problems?
4. What other factors might influence the rate at which medication leaves the body?
5. How would the answer change if the decay rate were different?

**Tip:** Exponential decay is common in processes where something decreases at a rate proportional to its current value, such as radioactive decay or population decline.

Some medicines can wear off in the body exponentially. In this case, assume the rate decays hourly for a starting amount of 500 mg of medication according to the equation: M = 500(0.89)^t. Solve this equation to determine the number of hours, t, that it will take for the initial 500 mg of medicine to decrease to 40 mg.

Solve an exponential decay problem involving medication wearing off in the body. The problem starts with 500 mg of medication and follows the equation M = 500(0.89)^t to determine when it will decrease to 40 mg. Learn how to use logarithms to find the number of hours. Suitable for Grades 10-12.

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