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?

Question

Mango

Mathematics

31 October, 14:01

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?

+2

Answers (1)

Know the Answer?

Bautista · 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.