Q. 12 - Precalculus Enhanced with Graphing Utilities

Question

Find an exponential function for the following graph.

Express your answer in the form $y = A.b^x$

Step-by-Step Solution

Answer

The exponential function is :$y = 2\times 3^x$

Step 1. Given Information

Step 2. Assume the function

let's assume the exponential function is,

$y=A\times b^x$

Now we get the given points through equation 

So, 

$2= A\times b^0$

$b^0= 1$

$A= 2$

Now the function is,

$y = 2\times b^x$

Step 3. Find the value of unknown constants

Now for x,

$6=2\times b^1$,

$$\begin{gathered} 6= 2\times b \\ b= 3 \end{gathered}$$

So, the function is $y= 2\times 3^x$