The price of oranges went from $.90 per lb to $1.20 per lb in 5 years. Find the rate of change of the price of oranges
1 answer:
recall that the average rate of change is simply the slope.
![\bf \begin{array}{|cc|ll} \cline{1-2} years&price\\ \cline{1-2} 0&0.90\\ 5&1.20\\ \cline{1-2} \end{array}~\hfill (\stackrel{x_1}{0}~,~\stackrel{y_1}{0.90})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{1.20}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1.20-0.90}{5-0}\implies \cfrac{0.30}{5}\implies \stackrel{\textit{6 cents per year}}{0.06}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7B%7Ccc%7Cll%7D%20%5Ccline%7B1-2%7D%20years%26price%5C%5C%20%5Ccline%7B1-2%7D%200%260.90%5C%5C%205%261.20%5C%5C%20%5Ccline%7B1-2%7D%20%5Cend%7Barray%7D~%5Chfill%20%28%5Cstackrel%7Bx_1%7D%7B0%7D~%2C~%5Cstackrel%7By_1%7D%7B0.90%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B5%7D~%2C~%5Cstackrel%7By_2%7D%7B1.20%7D%29%20%5C%5C%5C%5C%5C%5C%20slope%20%3D%20m%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%7B%20y_2-%20y_1%7D%7D%7B%5Cstackrel%7Brun%7D%7B%20x_2-%20x_1%7D%7D%5Cimplies%20%5Ccfrac%7B1.20-0.90%7D%7B5-0%7D%5Cimplies%20%5Ccfrac%7B0.30%7D%7B5%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7B6%20cents%20per%20year%7D%7D%7B0.06%7D)
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