Question

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?

Answer 1

Population = 10,000 x 2y 
y = periods of 14 years 

10,000 x (2 x 4) 
10,000 x 8 = 80,000

Population = 80,000 and the function is exponential  

Answer 2

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 $y=ab^x$

Now using both point to find a and b

$10000=a\cdot b^0\Rightarrow a=10000$

Using point (14,20000) and a=10000 to solve for b

$20000=10000\cdot b^{14}$

$2=b^{14}$

$b=2^{1/14}$

Exponential function:

$y=10000(2)^{\frac{x}{14}}$

We need to find y at x=42

So, we put x=42 into function and solve for y

$y=10000(2)^{\frac{42}{14}}$

$y=10000(2)^3$

y=80,000

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