Question

The population of Greenville is represented by the function f(x)=32,000×(0.9)^x, where x is the number of years since 2010. The population of Blueville was 35,000 in 2010, and has decreased exponentially at a rate of 15% each year. How do the populations of these cities compare in 2015? ___________.

Answer 1

In 2015, the population of Greenville is about 1.21 times the population of Blueville.

How did we get the value?

Let's calculate the populations for both Greenville and Blueville in the year 2015 (x = 5).

For Greenville:

`\[ f(5) = 32,000 * (0.9)^5 \]`

f(5) = 32,000 x 0.59049

f(5) = 18,849.28

For Blueville:

`\[ g(5) = 35,000 * (0.85)^5 \]`

g(5) = 35,000 x 0.443705

g(5) = 15,584.675

Therefore, in the year 2015, the population of Greenville is approximately 18,849.28, and the population of Blueville is approximately 15,584.675.

Now, to compare the populations, you can either subtract one from the other to find the difference or calculate the ratio of one to the other. If you're interested in the ratio:

`\[ \text{Ratio of Greenville to Blueville} = (f(5))/(g(5)) \]`

`\[ \text{Ratio} \approx (18,849.28)/(15,584.675) \]`

`\[ \text{Ratio} \approx 1.21 \]`

So, in 2015, the population of Greenville is about 1.21 times the population of Blueville.