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

D)80,000; exponential function

Step-by-step 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 :

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 :

Where a is Initial Population = 10,000

b is rate of change

x = time = 3 times

So, the population will be in 42 years=

                                                             =

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

Thus Option D is correct.

D)80,000; exponential function

c.

step-by-step explanation: