Question

an organisms population in the year 2000 was about 9 billion and was increasing with a double time of 20 years. Suppose the population continued this growth pattern from the year 2000 into the future. Complete part a through d

Answer 1

For this case we know that at the starting year 2000 the population was 9 billion and we also know that increasing with a double time of 20 years so we can set up the following model:

`18 =9(b)^20`

And if we solve for b we got:

`2 = b^20`

`2^(1/20)= b`

And then the model would be:

`y(t) = 9 (2)^{(t)/(20)}`

Where y is on billions and t the time in years since 2000.

And for this equation is possible to find the population any year after 2000

Explanation:

For this case we know that at the starting year 2000 the population was 9 billion and we also know that increasing with a double time of 20 years so we can set up the following model:

`18 =9(b)^20`

And if we solve for b we got:

`2 = b^20`

`2^(1/20)= b`

And then the model would be:

`y(t) = 9 (2)^{(t)/(20)}`

Where y is on billions and t the time in years since 2000.

And for this equation is possible to find the population any year after 2000