Question

if the price of a gallon in 1940 was $0.18 and $3.10 in 2010,the percentage rate of change for a gallon of gasoline over this period was

Answer 1

Answer: About 4.17%

Step-by-step explanation:

Given: The price of a gallon of gasoline in 1940 = $0.18

The price of a gallon of gasoline in 2010 = $3.10

Change in period : $2010-1940=70$

Change in price over the period :  $\ 3.10-\ 0.18=\ 2.92$

Now, the percentage rate of change of price for a gallon of gasoline over this period is given by :-

$\dfrac{\text{Change in price over period}}{\text{Change in period}}\times100\\\\\\=\dfrac{2.92}{70}\times100=4.17142857143 \approx4.17\%$

Hence, the  percentage rate of change of price for a gallon of gasoline over this period was 4.17 %.

Answer 2

$\bf \begin{array}{llll} slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies &\cfrac{2010-1940}{3.10-0.18}\\ &\qquad \uparrow \\ &\textit{rate of change} \end{array}$