A city's population, P (in thousands), can be modeled by the equation P = 130 (1.03) ^x where x is the number of years after January 1, 2000. For what value of x does the model predict that the population of the city will be approximately 170,000?

Question

Mathematics

Angeline Wells

10 June, 22:39

A city's population, P (in thousands), can be modeled by the equation P = 130 (1.03) ^x where x is the number of years after January 1, 2000. For what value of x does the model predict that the population of the city will be approximately 170,000?

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Answers (1)

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Carsen Griffith · Answer 1

To determine the value of x or the number of years, we need a function that would relate the population and the number of years since it only the population the value that is given. From the problem statement, the function would be expressed as follows:

P = 130 (1.03) ^x

We use this expression by simply substituting the population, P, to the function and solving for the number of years, x. We do as follows:

P = 130 (1.03) ^x

170000 = 130 (1.03) ^x

170000 / 130 = 1.03^x

x = 242.77

Therefore, the population would reach about 170000 after approximately 243 years.