Video: Evaluating Exponential Functions in a Real-World Context

Several fish were accidentally released into a lake. After 𝑛 weeks, the number of fish is estimated to be 𝑓(𝑛) = 59(1.1)^𝑛. Determine the likely number of fish in the lake after 5 weeks. Give your answer to the nearest whole number.

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Video Transcript

Several fish were accidentally released into a lake. After 𝑛 weeks, the number of fish is estimated to be 𝑓 of 𝑛 equals 59 times 1.1 to the 𝑛 power. Determine the likely number of fish in the lake after five weeks. Give your answer to the nearest whole number.

What information are we given? We’re given this exponential function. We can use this function to estimate the number of fish in the lake compared to the number of weeks the fish have been in there. We wanna estimate how many fish will be in the pond after five weeks.

We substitute five for the 𝑛 value. We then take 1.1 to the fifth power. If you plug that into your calculator, you’ll get 1.61051. And we can multiply that number by 59. Once we multiply that, we’re left with 95.02009.

Our question is asking for the estimate to the nearest whole number. We can round this to 95 and estimate that there will be around 95 fish in the lake after five weeks.

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