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?


2. The charge across a capacitor at any time t is given by:

                    q = e-0.02t(0.05cos 2t)

    Find the current in the circuit.


3. A particle moves along a straight line according to:

                    s = 2e3t + 5e-3t

    Find equations for the velocity and acceleration of the particle.


4. The current in a circuit is given by:

                    i = 4t2e8/t

    Find the times when the current is a minimum or maximum.


5. Exhaust fans are ventilating a room such that the number of cubic feet of CO2 in the room after t minutes is n = 3(e-0.05t + 1). what is the rate of change of n?


6. A casting is taken from one oven at 1500F and placed into another at 0F, but rising at a rate of 100o/hr. The temperature is then:

                T = 100t + 1500e-0.2t

Find the minimum temperature and when it occurs.


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