Let `y=f(x)=ab^x` represents the general form of the exponential function,
When a`>0` and b`>0` , b represents the growth factor,
When x=0 , then y=a which is the y-intercept.
2) Finding Grwoth factor and y-intercept from the table
Now let's have a sample table stated below to find out the y-intercept and growth factor.
If there is x value in the table having x=0 , then the corresponding y value represents the y-intercept, otherwise y-intercept can be found as follows:
Since the exponential function passes through the above points say (x_1,y_1) and (x_2,y_2), the points will satisfy the equation of the function,
`:.y_1=ab^(x_1)` -----equation 1
Dividing the above equations will yield,
Now from the table , plug in the values of the points to find the b,
Now y-intercept (a) can be found by plugging in any of the equation,
Let's plug b in the equation 1
3) Finding y-intercept and growth rate from the graph
Pl see the attached graph.
Look at the graph, y-intercept will be the y-coordinate where the graph of the function intersects the y-axis.
From the graph y-intercept=3
Growth factor can be found by noting the x and y-coordinates and then plugging them in the equation as follows:
From the graph,
So growth factor=`(y_2/y_1)^(1/(x_2-x_1))`