A 100-liter tank initially full of water develops a leak at the bottom. Given that 10% of the water leaks out in the first 5 minutes, find the amount of water left in the tank 20 minutes after the leak develops if the water drains off at a rate that is proportional to the amount of water present.

And we want to find the amount remaining after t = 20 minutes so we just need to replace into the model and we got:

Step-by-step explanation:

For this case if we assume the proportional model we have the following differential equation:

Where A represent the amount in the tank, t the time and k the proportional constant.

We can reorder the differential equation like this:

If we integrate both sides we got:

Using exponential on both sides we got:

And for this case  we have the following conditions given:

Using the first condition we have that:

Using the second condition we have:

And we can solve for k like this:

So then our model would be given by:

And we want to find the amount remaining after t = 20 minutes so we just need to replace into the model and we got: