Question

The population of a certain island has an annual growth rate of 6.9%. If you start with a poplulation of 2500 people, what would the population be in 10 years? Round your answer to the nearest hundred.

The population would be about

Answer 1

Po = 2500
r = 6.9% = 0.069
t = 10

P = Po * e^(rt)

= 2500*e^(0.069*10)
=2500*1.994
=4984.289
=4984 or approximately 5000

Answer 2

Hence, the population would be about 4872 after 10 years.

Explanation:

It is given that:

The population of a certain island has an annual growth rate of 6.9%.

This implies the population is growing at 0.069 times the previous population.

Hence, this situation could be modeled with the help of a population function P(t) as:

P(t)=p(1+0.069)^t

where p is the initial population of the island.

and t is the number of years.

Here we have p=2500.

and we are asked to find the value of the function P(t) at t-10.

The value is calculated as:

`P(t)=2500* (1.069)^(10)`

which approximately gives:

P(t)=4872.11

Hence, the population would be about 4872 after 10 years.