Question

one hundred grams of cane sugar in water are being converted into dextrose at a
rate which is proportional to the amount unconverted find the differential equation expressing the rate of conversion after t minutes

Answer 1

Answer on Question #78436 – Math – Differential Equations

Question

One hundred grams of cane sugar in water are being converted into dextrose at a rate which is proportional to the amount unconverted. Find the differential equation expressing the rate of conversion after $t$ minutes.

Solution

Let $m$ be the amount (in grams) of sugar converted in time $t$ (in minutes).

Then $(100 - m)$ is the amount (in grams) unconverted.

The rate of conversion is proportional to the amount unconverted

$$\text{the rate of conversion} = \frac{dm}{dt} = k(100 - m),$$

where $k$ is the constant of proportionality.

Answer: $\frac{dm}{dt} = k(100 - m)$.

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