Answer:
The rate of study is 5 items per hour.
Step-by-step explanation:
Number of items a person can learn after t hours of instruction, w(t) is given by:
[tex]w(t)=15\sqrt[3]{t^{2}}[/tex]
We want to determine the rate of learning at any time t. The rate is the derivative of w(t) with respect to time.
[tex]\frac{dw(t)}{dt} =\frac{d}{dt} 15\sqrt[3]{t^{2}}[/tex]
[tex]\frac{dw(t)}{dt} =15\frac{d}{dt} {t^{2/3}}[/tex]
[tex]\frac{dw(t)}{dt} =15X\frac{2}{3} {t^{2/3-1}}[/tex]
[tex]\frac{dw(t)}{dt} =10 {t^{-\frac{1}{3} }}=\frac{10}{t^\frac{1}{3}}[/tex]
Therefore, the rate of learning at any time t
[tex]\frac{dw(t)}{dt} =\frac{10}{t^\frac{1}{3}}[/tex]
At the end of 8 hours, t=8
[tex]\frac{dw(t)}{dt} =\frac{10}{8^\frac{1}{3}}[/tex]
[tex]\frac{dw(t)}{dt} =\frac{10}{2}[/tex]=5
The rate of study is 5 items per hour.
