Stitz-Zeager_College_Algebra_e-book

# Equation 71 the standard equation of a circle the

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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 thirty-fourth year to the end of the thirty-ﬁfth 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 thirty-fourth and thirty-ﬁfth 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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