Section 2.4.

Question:  1.  How long will it take an investment of $1000 to reach $3000 if it is compounded annually at 4%?

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How long will it take if compounded quarterly at the same annual rate?

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How long will it take if compounded continuously at the same annual rate?

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Question:  2.  What annual rate of return is required if an investment of $1000 is to reach $3000 in 15 years?

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Question:  3.  A bacteria colony has a constant growth rate.  The population grows from 40 000 to 100 000 in 72 hours.  How much longer will it take the population to grow to 200 000?

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Question:  4.  A population experiences growth rate k and migration rate M, meaning that when the population is P the rate at which new members are added is k P, but the rate at they enter or leave the population is M (positive M implies migration into the population, negative M implies migration out of the population).  This results in the differential equation dP/dt = k P + M.

Given initial condition P = P_0, solve this equation for the population function P(t).

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In terms of k and M, determine the minimum population required to achieve long-term growth.

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What migration rate is required to achieve a constant population?

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Question:  5.  Suppose that the migration in the preceding occurs all at once, annually, in such a way that at the end of the year, the population returns to the same level as that of the previous year.

How many individuals migrate away each year?

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How does this compare to the migration rate required to achieve a steady population, as determined in the preceding question?

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Question:  6.  A radioactive element decays with a half-life of 120 days.  Another substance decays with a very long half-life producing the first element at what we can regard as a constant rate.  We begin with 3 grams of the element, and wish to increase the amount present to 4 grams over a period of 360 days.  At what constant rate must the decay of the second substance add the first?

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