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=42
So, 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=80,000
Thus, 80,000 will be the population in 42 years. It is an exponential function.
