Question

Write an exponential function in the form y = ab that goes through points (0,18) and (3,6174).

Answer 1

Using the first point given in the statement you can find a, like this

`\begin{gathered} y=ab^x \\ \text{ Replace x = 0 and y = 18} \\ 18=ab^0 \\ 18=a\cdot1 \\ 18=a \end{gathered}`

Now, since you already have the value of a, you can find the value of b using the second point, like this

`\begin{gathered} y=ab^x \\ \text{ Replace x = 3 and y = 6174} \\ 6174=18\cdot b^3 \\ \text{ Divide by 18 into both sides of the equation} \\ (6174)/(18)=(18\cdot b^3)/(18) \\ 343=b^3 \\ \text{ Apply cube root to both sides of the equation} \\ \sqrt[3]{343}=\sqrt[3]{b^3} \\ 7=b \end{gathered}`

Therefore, the exponential function that passes through the points (0,18) and (3,6174) is

`y=18\cdot7^x`