Question

I have 4 questions I need help with This is first question number 2

Answer 1

We have the next function that models the Australian GDP since 1960 :

`G(i)=1806x(1.037)^t`

Where t is the number of years since 1960.

a)If we are in the year 1960, it means t=0

Therefore:

`G(t)=1806x(1.037)^1`
`G(0)=1806x(1.037)^0`
`G(0)=1806`

b)Now, we need to find the Australia capita in 1963.

This means t=3

Therefore:

`G(t)=1806x(1.037)^t`
`G(3)=1806x(1.037)^3`
`G(3)=2013.974721`

c) We need to find when the function is equal to 100,000.

Therefore we equal the function G(t)=100,000.

Then:

`1806x(1.037)^t=1000000`

Solve for t:

Divide both sides by 1806:

`(1806x(1.037)^t)/(1806)=(100000)/(1806)`
`(1.037)^t=(50000)/(903)`

Add Ln for each side:

`\ln (1.037)^t=in((50000)/(903))`
`t\ln (1.037)=in((50000)/(903))`

Then:

`t=(in((50000)/(903)))/(\ln (1.037))`
`t=110.48286`

Rounded to the nearest year:

`t=110`

Therefore: 1960 +110 = 2070

On 2070 the Austranlian GDP reaches 100,000 USD