29) a tank contains 100 gallons of water in which 40 pounds of salt are dissolved. it isdesired to reduce the concentration of salt to 0.1 pounds per gallon by pouring in purewater at the rate of 5 gallons per minute and allowing the mixture (which is kept uniformby stirring) to flow out at the same rate. how long will this take

The amount of salt in the tank at time , denoted by , changes over time according to the differential equation,

Multiply both sides by :

Now the left side can be condensed to the derivative of a product:

Integrate both sides to get

and solving for gives

Given that there are 40 pounds of salt at the start, or , we know , so that

We want the concentration to fall to 0.1 lb/gal, which means

so it would take about 73.78 minutes, or about 1.23 hours, for the concentration to fall to 0.1 lb/gal.

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!