Find the equation of the exponential function represented by the table below: 0 0.01 1 0.04 2 0.16 3 0.64
To find the equation of the exponential function represented by the given table, we need to determine the general form of an exponential function and then find the specific values based on the table.
The general form of an exponential function is given by y = ab^x, where "a" is the initial value or y-intercept when x = 0, and "b" is the base or growth/decay factor.
Let's substitute the given x and y values from the table into the exponential function:
For x = 0, y = 0.01:
0.01 = ab^0
0.01 = a
For x = 1, y = 0.04:
0.04 = ab^1
0.04 = ab
For x = 2, y = 0.16:
0.16 = ab^2
For x = 3, y = 0.64:
0.64 = ab^3
We now have a system of equations:
0.01 = a
0.04 = ab
0.16 = ab^2
0.64 = ab^3
We can solve this system of equations simultaneously to find the values of "a" and "b".
From the first equation, a = 0.01.
Substituting back into the second equation:
0.04 = (0.01)b
0.04/0.01 = b
b = 4
Now, we have the values "a" = 0.01 and "b" = 4.
The equation of the exponential function represented by the given table is:
y = 0.01 * 4^x