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.
To find the estimated average rate of change of the graphed quadratic function over the interval [2,6], we can use the formula:
Average Rate of Change = (f(6) - f(2)) / (6 - 2)
Let's say the graphed quadratic function is represented by the equation y = ax^2 + bx + c. We can find the values of a, b, and c from the graph or the given information.
Once we have the equation of the quadratic function, we can substitute the values of x = 6 and x = 2 to find f(6) and f(2). Plugging these values into the equation and calculating the difference, we can find the estimated average rate of change.
For the exponential function y = (3/4)(2)^x, the average rate of change over the interval [2,6] can be found similarly using the formula:
Average Rate of Change = (f(6) - f(2)) / (6 - 2)
Substituting the values of x = 6 and x = 2 into the exponential function, we can find the values of f(6) and f(2). Calculating the difference and dividing by the interval length will give us the average rate of change.
Comparing these two average rates of change will give us information about the steepness or growth rate of the quadratic and exponential functions over the interval [2,6].