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  

  $f(4) = 530$

Step-by-step explanation:

From the question we are told that

                 $f(t) = \frac{6000}{1 + Be^{-kt}}$

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

                     $f(0) = \frac{6000}{1 + Be^{-k(0)}}$

                    $300 = \frac{6000}{1 + Be^{-k(0)}}$

                    $1 + B = 20$

=>                  $B = 19$

So the above  equation becomes

               $f(t) = \frac{6000}{1 + 19 e^{-kt}}$

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

     So

           $f(2) = \frac{6000}{1+19e^{-2k}}$

            $400 = \frac{6000}{1+19e^{-2k}}$          

            $1+ 19 e^{-2k} = 15$

            $19 e^{-2k} = 14$

            $e^{-2k} = 0.7368$

           $-2k =-0.3054$

            $k = 0.1527$                

So the equation is now

       $f(t) = \frac{6000}{1+ 19e^{-0.1527t}}$

Now  at  t =  4 hrs we have that

      $f(4) = \frac{6000}{1+ 19e^{-0.1527* 4}}$

      $f(4) = 530$