Question

The town of Bertsville increased from a population of 3562 people in 1970 to a population of 9765 in 2000. Assume the growth was exponential

a. Define an exponential function that models the towns population as a function of the number of years since 1970.
=
b. What is the annual percent change?
%
c. Use your function to predict the town's population in 2019.

d. According to your function, in what year will the town's population reach 40000 people?

Answer 1

9765 = 3562 * x^30
x^30 = 2.7414
x = 1.0342
a ) An exponential function is:
y = 3562 * (1.0342)^n
b ) The annual percent change is:
1.0342 - 1 = 0.0342 = 3.42 %
c ) In 2019 :
n = 2019 - 1970 = 49
y = 3562 * (1.0342)^49 = 3562 * 5.195 = 18,506
d ) 40,000 = 3562 * (1.0342)^n
1.0342^n = 11.22964
n = 72
1970 + 72 = 2042
The town`s population will reach 40,000 people in 2042.