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In this lesson, we will learn how to solve real-world problems on exponential growth, such as population growth and compounded interest.

Q1:

The population of bacteria found in raw milk cheeses was found to increase by a factor of 10 after 10 hours at a temperature of 3 3 β C .

If the population started at 50 bacteria, how long would it take it to reach 300 bacteria, assuming exponential growth? Give the answer in hours and minutes.

How long would it take for the number of bacteria to double?

Q2:

In a laboratory, a bacteria population quadruples every hour. The population was first measured to be 50 bacteria. Write an equation that can be used to find π΅ , the bacteria population after π‘ hours.

Q3:

When caffeine is metabolized by our body (that is, when our body breaks down, uses, and absorbs caffeine), the decreasing quantity of caffeine can be modelled by the following function π = π π 0 β 0 . 1 π‘ , where π‘ is the number of hours after an intake of π 0 . What is the half-life of caffeine in our body (that is, how long does it take for our body to break down half of the caffeine)? Round your answer to the nearest hour.

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