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25 March, 23:26

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?

+1
Answers (1)
  1. 26 March, 01:39
    0
    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.
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