Question

If a city that currently has a population of 1000 triples in size every 8 years, what will the population be in 24 years and is the population growth modeled by a linear function or an exponential function?

Answer 1

24 years=8+8+8 3 times tripled
So 1,000×3^(3)=27,000

Answer 2

After 24 years population of the city will be 27000.

Explanation:

Since the population of a city gets tripled in 8 years means the sequence formed is an exponential function.

Now the function will be
`P=P_(0)(r)^(kt)`

Here P = Population after time t

P0 = initial population

r = common ratio

k = constant

t = period

Now we put the values in the equation.

`3000=1000(3)^(8k)`

`3^(1)=3^(8k)`

8k = 1

`k=(1)/(8)`

Now we have to find the population after 24 years

`P=1000(3)^{(24)/(8)}=1000(3)^(3)=27000`

Therefore after 24 years population of the city will be 27000.