Differential Equations question (1 Viewer)

[somerandomperson]

too much information, how do?

 

[ultra908]

u need to form an differential equation first. Let M be the amount of radioactive substance in the tank. Since water flows in and out of the tank at the same rate, the volume of the tank never changes.
5L of solution is flowing out- i.e. 5 * M/100 = 0.05M of radioactive substance. the substance is also decaying at a rate of 0.1M.
Thus dM/dt= -0.05M -0.1M = -0.15M. Then solve the DE.

 

[CM_Tutor]

It's an atypical problem, usually tanks don't include decay but have some amount flowing in and some other amount flowing out.

These can also be extended (though a question would need to be constructed carefully to not go beyond the syllabus) as an exploration of pollution control. For example, pollution flows in, diluted and flows out... it could then flow to a second tank where a similar process occurs. Given the syllabus seems to be presenting rates of change with a more environmental slant, I see such a question as a possibility, though I guess more at MX2 level.

For those interested, this further extends into predator-prey problems, where you have two animals whose population levels change a rate determined by each of their numbers. Tank problems can also be set up this way, such as with a chemical flowing into a tank containing bacteria that consume it.

 

[somerandomperson]

u need to form an differential equation first. Let M be the amount of radioactive substance in the tank. Since water flows in and out of the tank at the same rate, the volume of the tank never changes.
5L of solution is flowing out- i.e. 5 * M/100 = 0.05M of radioactive substance. the substance is also decaying at a rate of 0.1M.
Thus dM/dt= -0.05M -0.1M = -0.15M. Then solve the DE.

shouldn't the -0.01 be a power because it is decaying?

 

[ultra908]

shouldn't the -0.01 be a power because it is decaying?

this a differential equation, so no. Itll be part of the power in the solution tho.

 

[somerandomperson]

this a differential equation, so no. Itll be part of the power in the solution tho.

I see, thanks for replying.

 

[CM_Tutor]

I see, thanks for replying.

Try rearranging



to



and then integrating...