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 #69664 – 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 $q$ be the amount (in grams) of sugar converted in $t$ minutes.

Then $(100 - q)$ is the number of grams unconverted.

The rate of conversion is given by the following formula:

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

where $k$ is the constant of proportionality.

Answer: $\frac{dq}{dt} = k(100 - q)$.

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