Question

Use the graph to answers the following 2 questions: 1. Write the equation in $y = {ab}^{x}$form for this graph. 2. Using th equation from #1, what is the value when x=4?

Answer 1

$y=ab^x$

In a equation in the exponential general form you have:

a is the y-intercetp: the value of the function when x is 0)

For the given function the y intercept is (0,5), then

a=5

$y=5b^x$

Use the given point (2,45) to find the value of b

y=45

x=2

$45=5b^2$

Divide both sides of the equation into 5:

$\begin{gathered} \frac{45}{5}=\frac{5}{5}b^2 \\ \\ 9=b^2 \end{gathered}$

Find the square root in both sides of the equation:

$\begin{gathered} \sqrt[]{9}=\sqrt[]{b^2} \\ \\ 3=b \end{gathered}$

Then, for the given function you have the next equation:

$y=5\cdot3^x$

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To find the value of the function when x=4 use the equation above, substitute the x for 4 and evaluate:

$\begin{gathered} y=5\cdot3^4 \\ y=5\cdot81 \\ y=405 \end{gathered}$

Then, when x=4 the value of the function is 405