Question

Asked Jan 23, 2019

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Number 1

Step 1

Use below steps to obtain the desired result: -

Let C(t)=the amount of dye(in grams) for any time t.

and let C'=difference between the input rate and output rate that is;

C'=rate Input-rate Output

rate in = 0 because the water is coming in but it does not contaain any dye with it.

and rate output=(C/200)*2 because (C/200) is the dye concentration and 2 is the rate at which it is leaving the tank.

Now we need to write a differential equation so that we can model that how the amount of dye change.

Below is the differential equation to model how the amount of dye changes

Step 2

On dividing both sides by C we will get below value: -

Step 3

Now on integrating both sides with respect to ‘t&rs...

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