A city's current population is 1,000,000 people. It is growing at a rate of 3.5% per year. The equation P=1,000,000 (1.035) ^x models the city's population growth where x is the number of years from the current year. In approximately how many years will the pooulation be 1,400,000? Round to nearest tenth

Question

Sharon Avery

Mathematics

26 April, 14:27

A city's current population is 1,000,000 people. It is growing at a rate of 3.5% per year. The equation P=1,000,000 (1.035) ^x models the city's population growth where x is the number of years from the current year. In approximately how many years will the pooulation be 1,400,000? Round to nearest tenth

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Jacob Sloan · Answer 1

To determine the number of years to reach a certain number of population, we need an equation which would relate population and the number of years. For this problem, we use the given equation:

P=1,000,000 (1.035) ^x

We substitute the population desired to be reached to the equation and evaluate the value of x.

P=1,000,000 (1.035) ^x

1400000=1,000,000 (1.035) ^x

7/5 = 1.035^x

ln 7/5 = ln 1.035^x

x = ln 7/5 / ln 1.035

x = 9.78

Therefore, the number of years needed to reach a population of 1400000 with a starting population of 1000000 would be approximately 10 years.