SOLUTION: Really need help with this question, please show detailed workings and many thanks. At an annual company dinner, the CEO announced that the company will be expanding its operati

Click here to see ALL problems on Exponential-and-logarithmic-functions

Question 1021925: Really need help with this question, please show detailed workings and many thanks.
At an annual company dinner, the CEO announced that the company will be expanding its operations into other regions in South America and are looking for employees willing to travel around the region. There were two hundred employees who attended the company dinner. Two hours later, 350 employees had heard of this new opportunity. The number of employees who learned of the new program t hours later is given by the function:
f(t)= 2500/(1+Be^(-kt))
1) Name the type of function given in the question.
2) Find the value of B and k.
3) Estimate the number of employees in the company.
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
The function is exponential
If I plot on the vertical axis
and on the horizontal axis,
then the points given are:
( 0, 200 )
( 2, 350 )
Where the form is:
( t, f(t) )
------------------

Plug in the 1st point:

(1)
( note that
-------------------------
Plug in the 2nd point:
(2)
------------------------------------
(1)
(1)
(1)
(1)
Plug this result into (2)
-------------------
(2)
(2)
(2)
(2)
(2)
Take the natural log of both sides
(2)
(2)
(2)
------------------

--------------
The number of employees woud be when
approaches infinity
( a very long time after company made announcement )

approaches zero

The number of employees in company is 2500
---------------
Check one of the given points:
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
Error due to rounding off, I think
Hop I got it -tough problem!