Algebra 2 | Unit 4 | Lesson 4: Representing Functions at Rational Inputs | Practice Problems

A bacteria population is tripling every hour. By what factor does the population change in \(\frac12\) hour?

A medication has a half-life of 4 hours after it enters the bloodstream. A nurse administers a dose of 225 milligrams to a patient at noon. Write an expression to represent the amount of medication, in milligrams, in the patient’s body at 1 p.m. on the same day.

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A medication has a half-life of 4 hours after it enters the bloodstream. A nurse administers a dose of 225 milligrams to a patient at noon. Write an expression to represent the amount of medication, in milligrams, in the patient’s body at 7 p.m. on the same day.

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The expression \(225 \boldcdot \left(\frac12\right)^{\frac52}\) represents the amount of medicine in the body some time after it is administered. What is that time?

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The number of employees in a company has been growing exponentially by 10% each year. By what factor does the number of employees change each month?

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The number of employees in a company has been growing exponentially by 10% each year. By what factor does the number of employees change every 3 months?

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The number of employees in a company has been growing exponentially by 10% each year. By what factor does the number of employees change every 20 months?

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The value of a truck decreases exponentially since its purchase. The two points on the graph shows the truck’s initial value and its value a decade afterward.

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Express the car’s value, in dollars, as a function of time \(d\), in decades, since purchase.

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Write an expression to represent the car’s value 4 years after purchase.

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