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? A) 30,000; linear function B) 60,000; exponential function C) 72,000; linear function D) 80,000; exponential function

Answer 1

Answer: D) 80000; exponential function

Explanation:

It would double 3 times in total; first from 10k to 20k, then from 20k to 40k, and finally from 40k to 80k. Hope this helps

Answer 2

D)80,000; exponential function

Explanation:

We are given that a town with a population of 10,000 doubles every 14 years

So, Initial Population = 10,000

Now we are given that what will the population be in 42 years

First determine how many times population will double :
`(42)/(14) = 3`

So, In 42 years it doubles three times .

Now Linear functions change at a constant rate per unit interval while An exponential function changes by a common ratio over equal intervals.

So, the given situation will be modeled by exponential function

So, Using exponential function :
`y=ab^x`

Where a is Initial Population = 10,000

b is rate of change

x = time = 3 times

So, the population will be in 42 years=
`10000 (2)^3`

=
`80000`

So, the population will be 80,000 after 42 years.

Thus Option D is correct.

D)80,000; exponential function