Final answer:
The population of a town growing at an exponential rate of 13% annually from a current population of 21 thousand is predicted to be approximately 60,565 residents in nine years. This can be derived using the exponential function y = Ab^x, where A is 21, b is 1.13, and x is 9.
Step-by-step explanation:
The question is asking us to determine the population of a town in nine years, given that the population today is 21 thousand and increases by an exponential rate of 13% each year. The exponential growth of the population can be represented by the function y = Ab^x, where A is the initial amount, b is the base representing the growth rate, and x is time in years. In this case, A equals 21 (in thousands), and b equals 1.13 (which is 100% + 13% growth).
To calculate the population in nine years, we would substitute x with 9 into the equation y = 21(1.13)^9. This will give us the future population of the town, which can be calculated as: y = 21(1.13)^9 ≈ 21(2.88403) ≈ 60.56463 thousand, or approximately 60,565 residents.
A graph of the population function would show a classic exponential curve, starting at 21 thousand and rising steeply as the years increase, following the 13% annual growth rate.