Video: Evaluating Exponential Equations Involving Exponential Growth

A mathematical model predicts that the population of a city, 𝑥 million, will be given by the formula 𝑥 = 2(1.22)^𝑛, where 𝑛 is the number of years from now. What does the model predict the population will be in 2 years’ time?

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Video Transcript

A mathematical model predicts that the population of a city, 𝑥 million, will be given by the formula 𝑥 equals two multiplied by 1.22 to the power of 𝑛, where 𝑛 is the number of years from now. What does the model predict the population will be in two years’ time?

Let’s look at the formula: 𝑥 equals two multiplied by 1.22 to the power of 𝑛. As we want to calculate the population in two years’ time, 𝑛 must be equal to two. Therefore, the population will be calculated by multiplying two by 1.22 squared or to the power two.

Typing this into the calculator gives us a population in two years’ time of 2.9768 million people. Rounding this answer to two decimal places gives us a population of 2.98 million.

We can use this model to predict the population over a longer period of time. For example, if we wanted to calculate the population in 10 years’ time, we could substitute the number 10 in for 𝑛 in the formula and multiply two by 1.22 to the power of 10. This could be repeated for any number of years moving forwards.

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