Download Section 11.3 Examples Example 1: Recall that a rational number is a

Spring 2013
Hunnell
Section 11.3 Examples
Example 1: Recall that a rational number
is a number that can be expressed in the form
a , where a, b are integers and b 6= 0. Every
b
number with a terminating or repeating decimal expansion is a rational number.
1. Use knowledge of geometric series to express
the number 0.512 as the ratio of two integers.
2. Do the same for 0.113 (This one is trickier).
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Example 2: The Multiplier Effect in Economics
Suppose an income tax cut of X dollars is created, with the result that Y % (sometimes called
the marginal propensity to consume) of the resulting extra income is spent and the rest is
saved (Y is called the marginal propensity to
consume, or MPC).
If X is 10 (in billions of dollars) and Y is 93%,
calculate the total amount of new spending generated as a result of the tax cut.
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Example 3: Drug Therapy
For most medications, the rate at which a person’s body eliminates an applied medication is
proportional to how much of the drug is in the
person’s system.
Suppose a patient receives 2 mg of a certain
drug each day and that the body will eliminate
25% of the amount present in the system each
day. Estimate the total amount of the drug
that will be present after extended treatment,
immediately after a dose is given.
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Example 4: Perpetuities
A perpetuity is a periodic sequence of payments that continue forever. The capital value
of a perpetuity is the sum of the present values
of all future payments.
Suppose a perpetuity promises to pay $1000
at the beginning of each month. Suppose the
interest rate is 15% compounded monthly. The
present value of $1000 in n months is
.15 −n
1000(1 +
) = 1000(1.0125)−n
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Find the capital value of the perpetuity.
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