Given the function with f(3)=127 and f(1)=95, determine the rate of change over the interval 1≤x≤3.
as always, the rate of change is ∆y/∆x. In this case, that's
(127-95)/(3-1) = 16
totaly lit
To determine the rate of change over the interval 1 ≤ x ≤ 3, we can use the formula for average rate of change, which is:
Average Rate of Change = (f(x2) - f(x1)) / (x2 - x1)
In this case, x1 = 1 and x2 = 3, and the corresponding function values are f(1) = 95 and f(3) = 127.
Plugging in these values into the formula, we get:
Average Rate of Change = (127 - 95) / (3 - 1)
Simplifying further, we get:
Average Rate of Change = 32 / 2
Finally, the rate of change over the interval 1 ≤ x ≤ 3 is 16.
To determine the rate of change over the interval 1≤x≤3, you need to find the difference in the function values at the endpoints of the interval and divide it by the difference in their respective x-values.
First, you'll need to calculate the difference in the function values:
f(3) - f(1) = 127 - 95 = 32
Next, calculate the difference in the x-values:
3 - 1 = 2
Finally, divide the difference in the function values by the difference in the x-values to get the rate of change:
Rate of change = (f(3) - f(1)) / (3 - 1) = 32 / 2 = 16
Therefore, the rate of change over the interval 1≤x≤3 is 16.