Question

How do you write an exponential function from ordered pairs?

Answer 1

To write an exponential function from ordered pairs, find the common ratio and use the general form of the exponential function.

Step-by-step explanation:

To write an exponential function from ordered pairs, you need to find the common ratio between the y-values. The general form of an exponential function is y = a * (r^x), where a is the initial value and r is the common ratio. Here are the steps to write an exponential function from ordered pairs:

1. Identify two ordered pairs (x1, y1) and (x2, y2).
2. Find the common ratio by dividing the y-values: r = y2 / y1.
3. Plug one of the ordered pairs and the common ratio into the general form of the exponential function: y = a * (r^x1).
4. Solve for the initial value, a, by substituting the x-value and y-value from the ordered pair into the function and solving the equation.

For example, if the ordered pairs are (1, 2) and (2, 8), the common ratio is 4. Substituting (1, 2) and 4 into the general form, we get y = a * (4^1). Solving for a, we get a = 2 / 4 = 0.5. Therefore, the exponential function is y = 0.5 * (4^x).