Question

According to one theory of learning, the number of items, w(t), that a person can learn after t hours of instruction is given by: w(t) = 15 3 t2, 0 ≤ t ≤ 64 Find the rate of learning at the end of eight hours of instruction.

Answer 1

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:

$w(t)=15\sqrt[3]{t^{2}}$

We want to determine the rate of learning at any time t. The rate is the derivative of w(t) with respect to time.

$\frac{dw(t)}{dt} =\frac{d}{dt} 15\sqrt[3]{t^{2}}$

$\frac{dw(t)}{dt} =15\frac{d}{dt} {t^{2/3}}$

$\frac{dw(t)}{dt} =15X\frac{2}{3} {t^{2/3-1}}$

$\frac{dw(t)}{dt} =10 {t^{-\frac{1}{3} }}=\frac{10}{t^\frac{1}{3}}$

Therefore, the rate of learning at any time t

$\frac{dw(t)}{dt} =\frac{10}{t^\frac{1}{3}}$

At the end of 8 hours, t=8

$\frac{dw(t)}{dt} =\frac{10}{8^\frac{1}{3}}$

$\frac{dw(t)}{dt} =\frac{10}{2}$=5

The rate of study is 5 items per hour.