Question

The population of a town is estimated to increase by 13% per year. The population today is 21,000. Draw an exponential graph y = Ab^x of the population function and determine what the population will be nine years from now.

A) y = 21000 × (1.13)^9
B) y = 21000 × (0.87)^9
C) y = 21000 × (1.13)^-9
D) y = 21000 × (0.87)^-9

Answer 1

The population growth can be modeled with the exponential function y = 21000 × (1.13)^9, reflecting a yearly increase of 13%. Nine years from now, the population is predicted to follow this function's estimation, identified as option A.

Step-by-step explanation:

The question involves an exponential growth function, which models the increase in the population of a town estimated to grow 13% per year. Given that the town's current population is 21,000, the function representing the population growth can be written in the form of y = Ab^x, where A is the initial amount (current population), b is the growth factor, and x is the time in years.

In this case, A = 21,000 and b is 1.13 (since an increase of 13% per year means the population is multiplied by 1.13 each year). If we want to look at the population after 9 years, we set x to 9. The equation becomes:

y = 21000 × (1.13)^9

To find the projected population after 9 years, we calculate:

y = 21000 × (1.13)^9

Therefore, the correct answer, representing the population in 9 years, is:

Option A) y = 21000 × (1.13)^9