Question

Find a formula for the exponential function of the form = ^ that passes through the points (−4, 19) and (7, 3).Round the value of the base of the exponential to 4 decimal places

Answer 1

We are given that the graph of the function passes through (-4,19), and (7,3), therefore:

`\begin{gathered} 19=ab^(-4), \\ 3=ab^7. \end{gathered}`

Dividing the second equation by the first one, we get:

`\begin{gathered} (3)/(19)=(ab^7)/(ab^(-4))=(3)/(19)=b^(7+4), \\ b^(11)=(3)/(19), \\ b=\sqrt[11]{(3)/(19)}. \end{gathered}`

Now, substituting the above result in the second equation, we get:

`\begin{gathered} a(\sqrt[11]{(3)/(19)})=3, \\ a=\frac{3}{(\sqrt[11]{(3)/(19)})^7}. \end{gathered}`

Rounding b to 4 decimal places, we get:

`\begin{gathered} \\ b\approx0.8455. \end{gathered}`

Answer:

`\begin{gathered} a=\frac{3}{(\sqrt[11]{(3)/(19)})^7}, \\ b=0.8455. \end{gathered}`