Use the table to answer the question. x f(x) 0 2,500 1 2,625 2 2,756.25 3 2,894.06 Find the exponential function f(x)=a⋅b^x represented by the table. (1 point)
The table shows the values of x and f(x) for an exponential function. To find the exponential function represented by the table, we can see that the value of f(x) is increasing as x increases. This indicates that the base of the exponential function, b, is greater than 1.
Now, we need to find the values of a and b. We can start by looking at the value of f(0) which is equal to 2,500. This gives us the equation:
f(0) = a * b^0 = a
So, a = 2,500.
Next, we can look at the ratio of f(x) to f(x-1) which should be equal to b. Let's calculate the ratio for x = 1:
b = f(1) / f(0) = 2,625 / 2,500 = 1.05
Similarly, we can calculate the ratio for x = 2:
b = f(2) / f(1) = 2,756.25 / 2,625 = 1.05
And for x = 3:
b = f(3) / f(2) = 2,894.06 / 2,756.25 = 1.05
Since the ratio is the same for all values of x, we can conclude that the value of b is 1.05.
Therefore, the exponential function represented by the table is:
f(x) = 2,500 * 1.05^x