Question

in 2005, a certain town in La Union has a population of 32, 400. Each year, the population increases at a constant rate of about 7%. a. What is the growth factor of the town? b. Determine an exponential equation that models the population growth Pint years. c. Using the equation in (b), determine the population of the town in 2010. d If the population continues to increase at the same rate, how many people will there be in 2020?

Answer 1

The town's growth factor is 1.07, representing a 7% annual increase. The equation P=32400*(1.07)^t models the town's population growth. The town's population was approximately 45,716 in 2010, and would be approximately 88,995 in 2020.

Step-by-step explanation:

The growth factor for a rate of increase of 7% is 1.07. This is because a growth factor of 1 represents 100% (the initial amount), and an additional 0.07 represents the 7% increase.

An exponential equation that models the population growth can be written as P = P0 * (1.07)^t, where P0 is the initial population, 1.07 is the growth factor, and t represents time in years. In this case, since the initial population (P0) in 2005 was 32,400, the equation becomes P = 32400 * (1.07)^t.

To find the population in 2010, we calculate P = 32400 * (1.07)^5, as 2010 is 5 years after 2005. Using this calculation, the population in 2010 is approximately 45,716.

To find the population in 2020, we calculate P = 32400 * (1.07)^15, as 2020 is 15 years after 2005. Using this calculation, the population in 2020 would be approximately 88,995.

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