Find the equation of the exponential function represented by the table below:
x
x
y
y
0
0
0.02
0.02
1
1
0.01
0.01
2
2
0.005
0.005
3
3
0.0025
0.0025
The general form of an exponential function is y = ab^x, where b is the base value and a is the initial value or y-intercept. We can use the first two data points (0, 0) and (1, 1) to find the values of a and b.
When x is 0, y is also 0:
0 = ab^0
0 = a
When x is 1, y is 1:
1 = b
So the equation of the exponential function is:
y = 0.01(1)^x
Or simply:
y = 0.01 * (base value)^x
To find the equation of an exponential function, we need to determine the base and the y-intercept.
Looking at the table, we can see that as x increases by 1, y is divided by 2. This suggests that the base of the exponential function is 1/2.
To find the y-intercept, we need to find the value of y when x is equal to 0. From the table, we can see that y is equal to 0 when x is equal to 0.
Putting these values together, the equation of the exponential function is y = (1/2)^x.