+63 The question I am having trouble with is this:
For the function \(f(x)=\sqrt{5x+7}\) which value is closest to the average rate of change from f(a)=16 to f(b)=25?
I used Desmos to answer this question. I graphed the function then graphed f(a)=16 and f(b)25. Line 16 crosses the function at point (49.8, 16). Line 25 crosses the function at point (123.6, 25). Now apply the rate of change formula and you’ll get the answer.
+9481 average rate of change from f(a) to f(b) = slope between the points (a, f(a)) and (b, f(b))
average rate of change from f(a) to f(b) = \(\frac{f(b)-f(a)}{b-a}\)
Let's find a using the information that f(a) = 16
\(f(a)\,=\,\sqrt{5a+7}\\~\\ 16=\sqrt{5a+7}\\~\\ 16^2\,=\,5a+7\\~\\ 256\,=\,5a+7\\~\\ 249\,=\,5a\\~\\ 49.8\,=\,a\)
Let's find b using the information that f(b) = 25
\(f(b)\,=\,\sqrt{5b+7}\\~\\ 25=\sqrt{5b+7}\\~\\ 625\,=\,5b+7\\~\\ 618\,=\,5b\\~\\ 123.6\,=\,b\)
average rate of change from f(a) to f(b) = \(\frac{f(b)-f(a)}{b-a}\)
average rate of change from f(a) to f(b) = \(\frac{25-16}{123.6-49.8}\)
average rate of change from f(a) to f(b) = \(\frac{9}{73.8}\)
average rate of change from f(a) to f(b) = \(\frac{5}{41}\)
