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By S S Cheng

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A given substance satisfies the exponential growth law (1). Show that the grapb of In V versus t is a straight line. 2. A substance x multiplies exponentially, and a given quantity of the substance doubles every 20 years. If we have 3 lb of substance x at the present time, how many lb will we have 7 years from now? 3. A substance x decays exponentially, and only half of the given quantity of x remains after 2 years. How long does it take for 5 lb of x to decay to lib? 7 The dynamics of tumor growth, mixing problems, and orthogonal trajectories 4.

The number of individuals increased rapidly at first, and then more slowly, until towards the fourth day it attained a maximum level of 375, saturating the test tube. 309 /375. ) Figure 2 compares the graph of p(t) predicted by Equation (4) with the actual measurements, which are de- noted by o. As can be seen, the agreement is remarkably good. In order to apply our results to predict the future human population of the earth, we must estimate the vital coefficients a and b in the logistic equation governing its growth.

However, several engineers then raised the question of whether the drums could crack from the impact of hitting the ocean floor. C. "We'll see about that," said the engineers. After performing numerous experiments, the engineers found that the drums could crack on impact if their velocity exceeded forty feet per second. The problem before us, therefore, is to compute the velocity of the drums upon impact with the ocean floor. To this end, we digress briefly to study elementary Newtonian mechanics.

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