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.

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation:

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116