College Algebra

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Exponential equations. An equation which involves the unknown or unknowns in the exponents is often called an exponential equation. Thus, 2' = 16 is an exponential equation .__logio_a;^ logio 6 Art. 123] EXPONENTIAL EQUATIONS 163 in X. In this simple example, the value of x can be obtained by inspection ; but a table of logarithms is, in general, of value in solving exponential equations.
Such equations arise in a variety of problems. For instance, at compound interest, the amount of one dollar
... at a nominal rate of 0.05 per annum is (see Problem 29, p. 160) ^=A+2:2?y dollars, in which t is the time in years and n is the number of times per year that interest is converted. We may also write '-[^^)-r When n is indefinitely increased, the interest is said to be con- verted continuously. It turns out that, in this case (see p. 194), where e is the base of natural logarithms.
Example : What will $1000 amount to in one year at 5% interest con- verted continuously ?
Solution : Let S be the amount of $ 1000 at the end of a year, then ^ = 1000e005, log S = log 1000 + 0.06 log e = 3.0217, iSf=$1051.


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