Question

North Carolina Population (6 points each)The following table shows North Carolina's population since the year 2000.Year, x2000201020138.0499.5359.850NC Population (inmillions), yComplete the table below.1. Line of Best Fit2. ScenarioQuestion #13. ScenarioQuestion #24. Solution From(3)Find the equationfor the exponentialline of best fit.Using yourequation from (1).predict the NCPopulation for theyear 2017Write an equation(do not solve) thatmodels how manyyears after 2000will NC's populationwould reach 14millionDetermine thesolution from theequation youcreated in (3)

Answer 1

In this problem we have a exponential growth function of the form

`y=a(b^x)`

where

y ----> is the population

x ---> number of years

b is the base of the exponential function

a is the initial value since year 2000

we have

a=8,049

substitute

`y=8,049(b^x)`

we have the ordered pairs

(10,9,535) and (13,9,850)

so

For x=10