Question
Use the attached image to answer the question. 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 = 3/4 (2)^x over the same interval.
A. 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].
B. 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].
C. 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].
D. 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].
A. 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].
B. 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].
C. 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].
D. 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].
Answers
Answered by
GPT-4o mini
To compare the estimated average rate of change of the quadratic function and the exponential function over the interval [2, 6], we will calculate the average rate of change for both functions.
1. **For the quadratic function**:
Let’s denote the quadratic function as \( f(x) \). The average rate of change over the interval [2, 6] is given by:
\[
\text{Average Rate of Change} = \frac{f(6) - f(2)}{6 - 2}
\]
2. **For the exponential function**:
The exponential function is given by \( g(x) = \frac{3}{4}(2^x) \). The average rate of change over the interval [2, 6] is:
\[
\text{Average Rate of Change} = \frac{g(6) - g(2)}{6 - 2}
\]
Now, you can plug in the specific values for each function at \( x = 2 \) and \( x = 6 \) to find the two average rates of change.
However, since I don't have the specific values from the image, I cannot calculate the exact average rates.
You will need to calculate \( f(6) \) and \( f(2) \) to find the average rate of change for the quadratic function and \( g(6) \) and \( g(2) \) for the exponential function. After computing those values, you can assess the differences to choose one of the options A, B, C, or D.
If you provide the values or point out specific properties of the quadratic and exponential functions over that interval, I can help you arrive at a more precise conclusion.
1. **For the quadratic function**:
Let’s denote the quadratic function as \( f(x) \). The average rate of change over the interval [2, 6] is given by:
\[
\text{Average Rate of Change} = \frac{f(6) - f(2)}{6 - 2}
\]
2. **For the exponential function**:
The exponential function is given by \( g(x) = \frac{3}{4}(2^x) \). The average rate of change over the interval [2, 6] is:
\[
\text{Average Rate of Change} = \frac{g(6) - g(2)}{6 - 2}
\]
Now, you can plug in the specific values for each function at \( x = 2 \) and \( x = 6 \) to find the two average rates of change.
However, since I don't have the specific values from the image, I cannot calculate the exact average rates.
You will need to calculate \( f(6) \) and \( f(2) \) to find the average rate of change for the quadratic function and \( g(6) \) and \( g(2) \) for the exponential function. After computing those values, you can assess the differences to choose one of the options A, B, C, or D.
If you provide the values or point out specific properties of the quadratic and exponential functions over that interval, I can help you arrive at a more precise conclusion.