Question

An exponential function follows a pattern of decay through the points (–2, 25), (–1, 5), and (0, 1). Determine the base of the function.

1) 5
2) –5
3) negative one fifth
4) one fifth

Answer 1

To determine the base of the exponential decay function from the points given, we find that the base is one fifth (1/5) after solving the corresponding system of equations.

Step-by-step explanation:

The student is dealing with an exponential decay function, which can be determined using the given points. The general form is f(x) = abx, where a is the initial value and b is the base of the exponential function.

Using the points given, we can create a system of equations:

• 25 = ab-2
• 5 = ab-1
• 1 = ab0 = a

Since ab0 simply equals a, we know that a = 1. Substituting this into the second equation gives us 5 = 1 * b-1, which simplifies to b = 1/5. Thus, the base of the exponential decay function is one fifth.