Applications of Exponential & Log Function Derivatives

1. The number of bacteria, N, in a certain culture grows exponentially according to: N = 10,000e^{0.1t} 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 = 2e^{3t} + 5e^{-3t}

Find equations for the velocity and acceleration of the particle.

4. The current in a circuit is given by:

i = 4t^{2}e^{8/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 CO_{2} 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 100^{o}/hr. The temperature is then:

T = 100t + 1500e^{-0.2t}

Find the minimum temperature and when it occurs.