Question

Find the possible equations for the exponential function show (pic attached)

Answer 1

The Solution:

Given the graph below:

We are required to find the possible equation for the exponential function represented by the given graph.

The required exponential function can be obtained by the formula below:

$y=a(b)^x\ldots eqn(1)$

Apply the initial values indicated in the given graph.

That is, (0,60), this means when x = 0, y = 60

Substituting these values in the formula above, we get

$\begin{gathered} 60=a(b)^0 \\ 60=a\text{ ( since any number raised to the power of zero is equal to 1 )} \\ a=60 \end{gathered}$

Similarly,

(2,15), this means when x = 2, y = 15

Substituting these values in the formula, we have

$\begin{gathered} 15=a(b)^2 \\ \text{ Recall:} \\ a=60 \\ \text{ Substituting 60 for a, we get} \\ 15=60b^2 \end{gathered}$

Dividing both sides by 60, we get

$\begin{gathered} \frac{15}{60}=\frac{60b^2}{60} \\ \\ \frac{1}{4}=b^2 \end{gathered}$

Taking the square root of both sides, we get

$\begin{gathered} \sqrt[]{b^2}=\sqrt[]{(\frac{1}{4}}) \\ \\ b=\pm\frac{1}{2}=\pm0.5 \end{gathered}$

So, the exponential function is:

$y=60(\pm0.5)^x$

Therefore, the correct answer is [option 1]