5) Suppose that electricity is draining from a capacitor at a rate proportional to the voltage V across its terminals and that, if t is measured in seconds, dV 1 V dt 50 How long will it take the voltage to drop to 25% of its original value?

A tree farm starts with ten trees. Tree growth is expected to follow logistic growth with a first-order growth rate constant of r = 0.16 yr ' to a maximum of 8,000 trees. Write the equation that relates the number of trees (N) to time (1). What are the values of No, r, and K? Plot the number of trees over time if no harvesting occurs. Go out to about 70 years. What is the maximum sustainable yield (MSY)? How long should you wait before harvesting at the MSY? Determine the standing crop. (The standing crop is the number of trees at steady state when harvesting at the MSY.)

Near the surface of the earth, a ball (with p = 0.1) is released from rest and its flight through the air offers resistance that is proportional to its velocity. How long will it take the ball to reach one-half of its terminal velocity? How far will it travel during this time?