Question

Question linked in pic

Answer 1

iven:

heere are given that the population in the year 2000 was 12000 and the growth rate is 7% per year.

xplanation:

ccording to the question:

For t =0 which is the year 2000:

`P(0)=12000`

For t = 1:

`P(1)=12000+7\%(12000)`

If we say r is the rate, then:

`\begin{gathered} P(1)=12000+r(12000) \\ P(1)=12000(1+r) \end{gathered}`

Then,

For t = 2:

`\begin{gathered} P(2)=12000(1+r)(1+r) \\ P(2)=12000(1+r)^2 \end{gathered}`

And,

For t = 3:

`P(3)=12000(1+r)^3`

Therefore our function should be:

(a):

he population function:

`P(t)=12000(1.07)^t`

Now,

(b):

ccording to the question:

2008 is 8 year from year 2000:

Therefore, t = 8:

Then,

Put the value 8 for t into the function (a):

`\begin{gathered} P(8)=12000(1.07)^t \\ P(8)=12000(1.07)^8 \\ P(8)=12000(1.718) \\ P(8)=20616 \end{gathered}`

inal answer:

`P(t)=12000*(1.07)^(t-2000)`