Unformatted text preview: onential and Logarithmic Functions 3. Our initial investment is $2000, so to ﬁnd the time it takes this to double, we need to ﬁnd t
when A(t) = 4000. We get 2000(1.0059375)12t = 4000, or (1.0059375)12t = 2. Taking natural
ln(2)
logs as in Section 6.3, we get t = 12 ln(1.0059375) ≈ 9.75. Hence, it takes approximately 9 years
9 months for the investment to double.
4. To ﬁnd the average rate of change of A from the end of the fourth year to the end of the
ﬁfth year, we compute A(5)−A(4) ≈ 195.63. Similarly, the average rate of change of A from
5−4
the end of the thirtyfourth year to the end of the thirtyﬁfth year is A(35)−A(34) ≈ 1648.21.
35−34
This means that the value of the investment is increasing at a rate of approximately $195.63
per year between the end of the fourth and ﬁfth years, while that rate jumps to $1648.21 per
year between the end of the thirtyfourth and thirtyﬁfth years. So, not only is it true that
the longer you wait, the more money you have, but also the longer you wait, the faster the
m...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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