If a town with a population of 10,000 doubles every 14 years, what will the population be in 42 years and is it modeled by a linear function or an exponential function?
Accepted Solution
A:
Answer:80,000 will be the population in 42 years. It is an exponential function.Step-by-step explanation:If a town with a population of 10,000 doubles every 14 years.Initial population of a town is 10,000 Point: (0,10000) It's double every 14 years. Point: (14,20000)Let us suppose exponential function [tex]y=ab^x[/tex]Now using both point to find a and b [tex]10000=a\cdot b^0\Rightarrow a=10000[/tex]Using point (14,20000) and a=10000 to solve for b [tex]20000=10000\cdot b^{14}[/tex][tex]2=b^{14}[/tex][tex]b=2^{1/14}[/tex]Exponential function:[tex]y=10000(2)^{\frac{x}{14}}[/tex]We need to find y at x=42So, we put x=42 into function and solve for y [tex]y=10000(2)^{\frac{42}{14}}[/tex][tex]y=10000(2)^3[/tex]y=80,000Thus, 80,000 will be the population in 42 years. It is an exponential function.