Exponential & Log Function Derivatives

Applications of Exponential & Log Function Derivatives

1. The number of bacteria, N, in a certain culture grows exponentially according to:    N = 10,000e0.1t where t is in hours.What is the rate of population increase at      a) t = 0?

    b) t = 100?

Solution:    What is known? What are we looking for? Write this in mathematical terms.

   N = 10,000e0.1t       and     dN/dt = ? when t = 0 and t = 100.

How do we get dN/dt?

    We take the derivative of N(t) with respect to time.

    dN/dt = (0.1)*10,000e0.1t   =  1000e0.1t

    Then dN/dt (t = 0) = 1000bacteria/hr

             dN/dt (t = 100) = 2.20 x 107 bacteria/hr

    Wow! Makes you want to go and wash your hands!