Ramona wants to use the table to prove something about how exponential functions grow. What does she need to do next and what will she be able to prove?
To prove something about how exponential functions grow using a table, Ramona needs to create a table of values for an exponential function.
Next, Ramona can calculate the values of the exponential function for different input values (usually x) as specified by her chosen equation. She can start with small values of x and gradually increase it to see how the function grows. For each value of x, she can evaluate the function to find the corresponding y-values.
By examining the values in her table, Ramona will be able to demonstrate the key characteristics of exponential growth:
1. Constant ratio: She will observe that the ratio of successive y-values remains approximately constant. In other words, if she divides any y-value by the preceding one, she will obtain a similar result.
2. Increasing rate: As the input values increase, the corresponding output values will increase, but at an accelerating rate. This means that the function grows faster and faster as x increases.
3. Steepness of the curve: Ramona will notice that the function's graph displays a steep upward slope, indicating the rapid growth.
By gathering this evidence from the table, Ramona can establish the pattern of exponential growth and provide quantitative evidence to support her claim or observation about how exponential functions grow.