Exponential Regression Notes

Exponential Regression Analysis

Given Data

• Population, P (in thousands) after n years:

  • n (years): 0, 3, 7, 12, 14, 19

  • P (population): 2400, 2495.96, 2756.85, 3135.09, 3166.75, 3321.53

Exponential Regression Equation

(a) Finding the Exponential Regression Model

• An exponential regression equation has the general form:
  $P = a imes b^n$
  where:

  • P: population (in thousands)

  • n: number of years

  • a: y-intercept (initial population growth value)

  • b: growth factor per year

• Upon calculation using a calculator:

  • Value of a: rounded to two decimal places

  • Value of b: rounded to three decimal places

Exponential Regression Equation Output

• The finalized model based on the data (inserted values):
  $P = a imes b^n$
  (Exact values need to be filled in based on the calculator output)

Percent Increase Per Year

(b) Calculating Percent Increase

• The percent increase per year based on the regression model is:

  • Percent Increase: 1.80%

Predicting Future Population

(c) Population Prediction at n = 20

• Using the regression model to find the population P when:

  • n = 20:

  • Substitute n into the equation to calculate P:
    $P = a imes b^{20}$

  • Round the answer to two decimal places:

  • Result:

  • P = (insert answer in thousands)

Interpretation of the Result

(d) Completing the Sentence

• For the interpretation of the result:

  • The population of the town after 20 years is (insert calculated population) thousand people.