Final answer:
The exponential function that passes through the points (0,7) and (2,112) can be determined to be f(x) = 7 × 4^x using the general form of an exponential function and solving for its base and coefficient.
Step-by-step explanation:
Finding an Exponential Function From Two Points
To find the formula for an exponential function that passes through the points (0,7) and (2,112), we can use the general form of an exponential function:
f(x) = abx
Since the function passes through the point (0,7), we substitute x with 0 and f(x) with 7:
7 = ab0 => 7 = a(1) => a = 7
Next, we use the point (2,112) to find the value of b. We substitute x with 2 and f(x) with 112:
112 = 7b2 => b2 = 16 => b = 4
The formula for the exponential function is therefore:
f(x) = 7 × 4x