Exponential Growth Problem

[jyoun125]

5. Spreading of a rumor. Three hundred college students attend a lecture of the Dean at which she hints that the college will become coed. The rumor spreads according to the logistic curve:

. . . . .\(\displaystyle Q(t)\, =\, \dfrac{3000}{1\, +\, Be^{-kt}}\)

where \(\displaystyle t\) is measured in hours.

a. Compute the parameter \(\displaystyle B.\)

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The problem is [above].

Please help!

 

[Ishuda]

How many people attended the lecture which is time zero. What is the value of the equation at time zero?

 

[jyoun125]

How many people attended the lecture which is time zero. What is the value of the equation at time zero?

I believe it is 300.

 

[Ishuda]

I believe it is 300.

So Q(t) is 300 when t=0, i.e.
\(\displaystyle 300 = \frac{3000}{1 + B e^{-k t} }\)
when t=0. So what is e^-kt at t=0 and what does mean about the equation?

 

[jyoun125]

So Q(t) is 300 when t=0, i.e.
\(\displaystyle 300 = \frac{3000}{1 + B e^{-k t} }\)
when t=0. So what is e^-kt at t=0 and what does mean about the equation?

It should equal one, correct? Because e^0=1.

 

[Ishuda]

It should equal one, correct? Because e^0=1.

Correct. So what is the form of the equation?

 

[jyoun125]

Correct. So what is the form of the equation?

So if e^0=1, then parameter B must equal 9 because to get 300 from 3000 you must divide it by 10. And 1+9(1)=10.

 

[Ishuda]

So if e^0=1, then parameter B must equal 9 because to get 300 from 3000 you must divide it by 10. And 1+9(1)=10.

Sounds good to me. Good work