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Rus_ich [418]
3 years ago
13

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.
Mathematics
1 answer:
Juli2301 [7.4K]3 years ago
4 0

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.

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