Question

Create the exponential function in the form f (x) = a(b) that fits the two data points given

(3, 40) & (11, 108)
8

Answer 1

To create an exponential function that fits the given data points (3, 40) & (11, 108), solve a system of equations to determine the values of a and b. The resulting exponential function is f(x) ≈ 0.044(1.442^x).

Step-by-step explanation:

To create an exponential function that fits the given data points, we need to find the values of a and b in the form f(x) = a(b^x). Let's use the first data point (3, 40) to solve for a:

40 = a(b^3)

Next, let's use the second data point (11, 108) to solve for b:

108 = a(b^11)

Now, we have a system of equations that can be solved simultaneously:

40 = a(b^3)

108 = a(b^11)

Solving this system of equations, we find that a ≈ 0.044 and b ≈ 1.442. Therefore, the exponential function that fits the two data points is f(x) ≈ 0.044(1.442^x).

Learn more about Creating an exponential function that fits two data points