Question

A student must learn M unfamiliar words for an upcoming test. The rate at which the student learns is proportional to the number of items remaining to be learned, with constant of proportionality equal to k. Initially, the student knows none of the words. Let y(t) stand for the number of the words that the student knows at time t.

Answer 1

dy/dt=k(M-y)
Don’t have time to think about the actual equation for y, but from this equation you should use separation of variables and integrate both sides. It should be an exponential equation.

Answer 2

The equation that represent the number of the words that the student knows at time t is y(t) = kt

Equation

An equation is an expression that is used to show the relationship between two or more variables and numbers.

Let y(t) represent the number of the words that the student knows at time t.

y ∝ t

y(t) = kt

Where k is the constant of proportionality

The equation that represent the number of the words that the student knows at time t is y(t) = kt

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