Use the image to answer the question.

A curve and two labeled points on the curve are plotted in quadrant 1 of a coordinate plane.

Given the graph of the exponential equation, write the correct exponential equation for the graph.

1 answer

To write the correct exponential equation for a graph, we typically need the form of the exponential function, which is usually represented as:

\[ y = ab^{x} \]

where:

  • \( y \) is the output,
  • \( x \) is the input,
  • \( a \) is a constant that represents the y-intercept (the value of \( y \) when \( x = 0 \)),
  • \( b \) is the base of the exponential function, which determines the rate of growth or decay.

To construct the specific equation given points from the graph, you would follow these general steps:

  1. Identify the y-intercept (if it is visible), which gives you the value of \( a \).
  2. Use the coordinates of the two points on the curve to form equations that allow you to solve for \( a \) and \( b \).

If you provide the coordinates of the labeled points on the curve or any specific details about the graph, I can help you formulate the exact exponential equation.