One model for the spread of a virusis that the rate of spread is proportional to the product of the fraction of the population P who have contracted the virusand the fraction who have not contracted the virus. a.Write out a differential equation that is satisfied by P. b.Solve the differential equation. c.Ina small communityof 100,000 inhabitants. At 8:00 am on the initial day of reporting, 100peoplehad contractedthe virus. By 8:00 am on the third day,200more people had contacted the virus. At what time will 90% of the population havecontracted the virus

The differential equation for the model is

The model for P is

At half day of the 4th day (t=4.488), the population infected reaches 90,000.

Step-by-step explanation:

We can write the rate of spread of the virus as:

We know that P(0)=100 and P(3)=100+200=300.

We have to calculate t so that P(t)=0.9*100,000=90,000.

Solving the diferential equation

Then the model for the population infected at time t is:

Now, we can calculate t for P(t)=90,000

At half day of the 4th day (t=4.488), the population infected reaches 90,000.

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step-by-step explanation:

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step-by-step explanation: