We know that the function is equal to 5 when x=0. Let's make a table of values using the given information.
We can say that the table represents an exponential function since the y-values change by a factor of 4 as x increases by 2. We know that any exponential function has the form below.
g(x)= a( b)^x
Here, a is the initial value, or y-intercept. b is the constant multiplier, as the x-variable increases by one. Let's make a table for the same function for consecutive x-values. Note that if the ratio between y-values when x increases by 2 is 4, then the ratio between y values when x increases by one is 4÷ 2=2.
Now we can see that as x increases by 1, the constant multiplier is 2. With this information and knowing that the y-intercept is 5, we can write the function rule.
g(x)= 5( 2)^x
