Question

In 1994 the city of Anoka had a population of 18,000 people. Since then the population has grown by 5.2% each year. In 1994 the city of Minneapolis had a population of 390,000 and has been decreasing by 2.3% each year. How many more people will be living in Minneapolis compared to Anoka after 25 years?

Answer 1

Answer:

After 25 years, Minneapolis will have 154,062 more residents than Anoka.

Step-by-step explanation:

First, let's write a function for each case.

For Anoka, the initial population is 18,000. The population grows 5.2% or 0.052 each year. Thus:

$A(x)=18000(1.052)^x$, where x represents the amount of years after 1994.

Inversely, for Minneapolis, the population decreases by 2.3% or 0.023. Another way to write this is that it in changes by 1-0.023 or .977 or 97.7%. Thus:

$M(x)=390000(0.977)^x$.

To find how many more people are living in Minneapolis than Anoka after 25 years, simply plug 25 into the functions and then subtract.

In Anoka, after 25 years, there will be:

$A(25)=18000(1.052)^{25}\approx 63924$ residents.

In Minneapolis, after 25 years, there will be:

$M(25)=390000(.977)^{25}\approx217986$ residents.

217986-63924=154,062 residents.