Question

After one week a music downloading site sold over 80,000 songs. After 4 weeks the music downloading site sold over 300,000 songs. Find the average rate of change of songs per week.

75,000 songs per week

80,000 songs per week

55,000 songs per week

73,334 songs per week

Answer 1

`\bf \begin{array}{ccll} \stackrel{x}{weeks}&\stackrel{y}{songs}\\ \cline{1-2} 1&80000\\ 4&300000 \end{array}~\hspace{10em} (\stackrel{x_1}{1}~,~\stackrel{y_1}{80000})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{300000}) \\\\\\ \stackrel{\textit{average rate of change}}{slope = m\implies} \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{300000-80000}{4-1}\implies \cfrac{220000}{3}\quad \approx \quad 73333`