To model the data using an exponential function f(x) = Ab^x, we need to find the values of A and b.
We can start by using the given data points to create a system of equations:
When x = 0, f(x) = 100
100 = Ab^0
100 = A
When x = 1, f(x) = 90
90 = Ab^1
90 = Ab
When x = 2, f(x) = 81
81 = Ab^2
We can use the first equation to solve for A and substitute that value into the second equation:
90 = Ab
90 = 100b
b = 0.9
Now we can substitute the values of A and b into the third equation to solve for A:
81 = Ab^2
81 = 100(0.9)^2 A = 100(0.81)
A = 81
Therefore, the exponential function that models the data is:
f(x) = 100(0.9)^x
or
f(x) = 81(0.9)^x