Question

In the year 2010, the population of a city was 600,000 citizens. The population increases at a rate of 1.8% per year.

a. Create a function and table to model the population y (in thousands), in terms of x years (form 2010 to 2020). (or the expression "with x being years from 2010 to 2020")
In complete sentences, interpret the table and its function. include if the data is linear or exponential and how that conclusion was reached.
b. Predict the population of the city in the year 2025.
In your final answer, be sure to include the table, interpretation, and prediction of the function.

Answer 1

a. The population of the city can be modeled using the exponential growth function:

y = 600(1 + 0.018)^x

with x being years from 0 to 10, where x = 0 corresponds to the year 2010. We can create a table to show the population for each year from 2010 to 2020:

(you can see above)

We can see from the table that the population of the city is increasing each year, and the rate of increase is accelerating. This is because the growth function is exponential, not linear. We know it is exponential because the function has a power of x in the exponent, which causes the rate of growth to increase over time. If the function were linear, the rate of growth would be constant.

b. To predict the population in 2025, we can use the same function with x = 15 (since 2025 is 15 years after 2010):

y = 600(1 + 0.018)^15

y ≈ 846.5 (in thousands)

Therefore, we can predict that the population of the city in 2025 will be approximately 846,500 citizens.