Question

f(x) = 500(1.05)x What was the average rate of change of the value of Sophia's investment from the second year to the fourth year?

Answer 1

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------\\\\ f(x)=500(1.05)^x \qquad \begin{cases} x_1=2\\ x_2=4 \end{cases}\implies \cfrac{f(4)-f(2)}{4-2} \\\\\\ \cfrac{[500(1.05)^4]~-~[500(1.05)^2]}{4-2}\implies \cfrac{56.503125}{2}\implies 28.2515625$