Question

Exponential from Two Points Level 1

Answer 1

First write the equation

`\begin{gathered} y=ab^x \\ (0,4)\text{ and (3,500)} \\ \text{when x = 0, y = 4} \\ 4=ab^0 \\ b^0\text{ = 1} \\ \text{Therefore} \\ 4\text{ = a x 1} \\ a\text{ = 4} \\ \text{when x = 3, y = 500} \\ 500=ab^3 \\ 500=4b^3 \\ \text{divide through by 4} \\ (500)/(4)=(4b^3)/(4)^{} \\ 125=b^3 \\ \text{Take cube root of both sides} \\ b\text{ = }\sqrt[3]{125} \\ b\text{ = 5} \end{gathered}`

Therefore, the exponential equation

`\begin{gathered} is\text{ } \\ y=4(5^x) \end{gathered}`