Question

In 2007 the population of the town of Cartersville was 24,455. The population growth can be represented by the formula P = 24,455(1.03)x, where x represents the number of years after 2007. When will the population of the town first exceed 30,000? A) 2011 B) 2012 C) 2013 D) 2014

Answer 1

2014, you're welcome!

Answer 2

The year in which the population of Cartersville will be more than 30,000 for the first time will be D. 2014.

What year will Cartersville pass 30,000 people?

Given the formula to find the population in a year, we can find the year the population exceeds 30,000 by solving for x.

The formula to find the year the population goes to 30,000 is:

30,000 = 24,455(1.03)^x

Solving gives:

30,000 / 24,455 = (1.03)^x

1.23 = 1.03^x

Log (1.23) = Log (1.03)x

x = Log (1.23) / Log (1.03)

= 7 years

The year will be:

= 2007 + 7

= 2014

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