Question

I need help with this question. Solve in y=a•b^x format

Answer 1

Solve the equation in this format:

`y=a\mathrm{}b^x`

when x = 0, y = 1000

`\begin{gathered} y=ab^x \\ 1000=a\mathrm{}b^0 \\ 1000=a\ldots\ldots\text{.}\mathrm{}(1) \end{gathered}`

when x = 2, y = 360

`\begin{gathered} y=a\mathrm{}b^x \\ 360=ab^2\ldots\ldots..(2) \end{gathered}`

solve the equation simulataneously

`\begin{gathered} 1000=a\ldots\ldots(1) \\ 360=ab^2\ldots....(2) \\ sub\text{ the value of a in equ(2)} \\ 360=1000b^2 \\ \text{divide both side by 1000} \end{gathered}`
`\begin{gathered} (360)/(1000)=(1000b^2)/(1000) \\ (36)/(100)=b^2 \\ \text{square the root of both side} \\ \sqrt[]{(36)/(100)}=\sqrt[]{b^2} \\ (6)/(10)=b \\ (3)/(5)=b \end{gathered}`

Therefore the equation of the function is

`\begin{gathered} y=a.b^x \\ y=1000.((3)/(5))^x \end{gathered}`