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} \frac{360}{1000}=\frac{1000b^2}{1000} \\ \frac{36}{100}=b^2 \\ \text{square the root of both side} \\ \sqrt[]{\frac{36}{100}}=\sqrt[]{b^2} \\ \frac{6}{10}=b \\ \frac{3}{5}=b \end{gathered}$

Therefore the equation of the function is

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