An exponential function is given by the equation y=3x . Using the points x
and x+1
, show that the y-values increase by a factor of 3 between any two points separated by x2−x1=1 .
Given the exponential function y = 3^x, let's calculate the y-values for x and x+1.
For x:
y(x) = 3^x
For x+1:
y(x+1) = 3^(x+1) = 3 * 3^x
Now, let's compare the two y-values:
y(x+1) / y(x) = (3 * 3^x) / 3^x = 3
This shows that the y-values increase by a factor of 3 between any two points separated by x2−x1 = 1.