Question

300 students attended the dedication ceremony of a new building on a college campus the president of the traditionally female college announced a new expansion programme which included plans to make the college co-educational the number of students who learnt of the new program t hours later is given by the function​

Answer 1

Complete Question

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Answer:

The number of student that have heard the announcement after 4 hours is

`f(4) = 530`

Explanation:

From the question we are told that

`f(t) = (6000)/(1 + Be^(-kt))`

Now at time t = 0 f(t) = 300 this because at the time the announcement was made the number of student present was
`f(0) = 300`

so

`f(0) = (6000)/(1 + Be^(-k(0)))`

`300 = (6000)/(1 + Be^(-k(0)))`

`1 + B = 20`

=>
`B = 19`

So the above equation becomes

`f(t) = (6000)/(1 + 19 e^(-kt))`

Now at the given time t = 2hr
`f(2) = 400`

So

`f(2) = (6000)/(1+19e^(-2k))`

`400 = (6000)/(1+19e^(-2k))`

`1+ 19 e^(-2k) = 15`

`19 e^(-2k) = 14`

`e^(-2k) = 0.7368`

`-2k =-0.3054`

`k = 0.1527`

So the equation is now

`f(t) = (6000)/(1+ 19e^(-0.1527t))`

Now at t = 4 hrs we have that

`f(4) = (6000)/(1+ 19e^(-0.1527* 4))`

`f(4) = 530`