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A U-shaped upward opening curve with 2 plotted points is on a coordinate plane. The x-axis ranges from negative 4 to 7 in increments of 1. The y-axis ranges from negative 3 to 15 in increments of 1.

Compare the estimated average rate of change of the graphed quadratic function over the interval [2,6]
to the average rate of change of the exponential function y=34(2)x
over the same interval.

(1 point)
Responses

The estimated average rate of change of the exponential function is 7.25 greater than the estimated average rate of change of the quadratic function over the interval [2,6]
.
The estimated average rate of change of the exponential function is 7.25 greater than the estimated average rate of change of the quadratic function over the interval left bracket 2 comma 6 right bracket.

The estimated average rate of change of the quadratic function is 0.16 greater than the estimated average rate of change of the exponential function over the interval [2,6]
.
The estimated average rate of change of the quadratic function is 0.16 greater than the estimated average rate of change of the exponential function over the interval left bracket 2 comma 6 right bracket.

The estimated average rate of change of the quadratic function is 7.25 greater than the estimated average rate of change of the exponential function over the interval [2,6]
.
The estimated average rate of change of the quadratic function is 7.25 greater than the estimated average rate of change of the exponential function over the interval left bracket 2 comma 6 right bracket.

The estimated average rate of change of the exponential function is 0.16 greater than the estimated average rate of change of the quadratic function over the interval [2,6]
.
The estimated average rate of change of the exponential function is 0.16 greater than the estimated average rate of change of the quadratic function over the interval left bracket 2 comma 6 right bracket.
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1 answer

To accurately compare the average rates of change of both the quadratic function and the exponential function over the interval [2, 6], I would need the specific values of the function at those points.

However, I can provide a general guide on how to calculate the estimated average rate of change for both functions:

  1. Quadratic Function: To find the average rate of change over the interval \([2, 6]\), use the formula: \[ \text{Average Rate of Change} = \frac{f(6) - f(2)}{6 - 2} \]

  2. Exponential Function: Similarly, for the exponential function \(y = 34(2)^x\): \[ \text{Average Rate of Change} = \frac{g(6) - g(2)}{6 - 2} \quad \text{where } g(x) = 34(2)^x \]

  3. Compare: After calculating both rates, you can compare them and see which one is greater and by how much.

Given that the question provides several comparison statements, you should compute the estimated values using the described methods. Once you have the average rates of change for both functions over the specified interval, you can choose the response that accurately reflects your findings.

If you have specific values (like the value of the quadratic function at x = 2 and x = 6, and the computed exponential function values) I can help you calculate and compare them directly.