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# 0410 ch 4 day 10

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• ### 0410 ch 4 day 10

1. 1. 4.4 Exponential & Logarithmic Equations Day 3Romans 15:13  May the God of hope ﬁll you withall joy and peace in believing, so that by the powerof the Holy Spirit you may abound in hope.
2. 2. \$2000 is invested at an interest rate of 3.5% per year.Find the time for the money to double if the interest iscompounded monthly.
3. 3. \$2000 is invested at an interest rate of 3.5% per year.Find the time for the money to double if the interest iscompounded monthly. nt ⎛ r ⎞ A = P ⎜ 1+ ⎟ ⎝ n ⎠
4. 4. \$2000 is invested at an interest rate of 3.5% per year.Find the time for the money to double if the interest iscompounded monthly. nt ⎛ r ⎞ A = P ⎜ 1+ ⎟ ⎝ n ⎠ 12t ⎛ .035 ⎞4000 = 2000 ⎜ 1+ ⎟ ⎝ 12 ⎠
5. 5. \$2000 is invested at an interest rate of 3.5% per year.Find the time for the money to double if the interest iscompounded monthly. nt ⎛ r ⎞ A = P ⎜ 1+ ⎟ ⎝ n ⎠ 12t ⎛ .035 ⎞4000 = 2000 ⎜ 1+ ⎟ ⎝ 12 ⎠ ⎛ .035 ⎞log 2 = 12t log ⎜ 1+ ⎟ ⎝ 12 ⎠
6. 6. \$2000 is invested at an interest rate of 3.5% per year.Find the time for the money to double if the interest iscompounded monthly. nt ⎛ r ⎞ A = P ⎜ 1+ ⎟ ⎝ n ⎠ log 2 =t ⎛ .035 ⎞ 12t 12 log ⎜ 1+ ⎟ ⎛ .035 ⎞ ⎝ 12 ⎠4000 = 2000 ⎜ 1+ ⎟ ⎝ 12 ⎠ ⎛ .035 ⎞log 2 = 12t log ⎜ 1+ ⎟ ⎝ 12 ⎠
7. 7. \$2000 is invested at an interest rate of 3.5% per year.Find the time for the money to double if the interest iscompounded monthly. nt ⎛ r ⎞ A = P ⎜ 1+ ⎟ ⎝ n ⎠ log 2 =t ⎛ .035 ⎞ 12t 12 log ⎜ 1+ ⎟ ⎛ .035 ⎞ ⎝ 12 ⎠4000 = 2000 ⎜ 1+ ⎟ ⎝ 12 ⎠ t ≈ 19.8 years ⎛ .035 ⎞log 2 = 12t log ⎜ 1+ ⎟ ⎝ 12 ⎠
8. 8. A sum of money invested at a ﬁxed rate with continuouscompounding tripled in 19 years. Find the rate.
9. 9. A sum of money invested at a ﬁxed rate with continuouscompounding tripled in 19 years. Find the rate. rt A = Pe
10. 10. A sum of money invested at a ﬁxed rate with continuouscompounding tripled in 19 years. Find the rate. rt A = Pe 19r 3 = 1e
11. 11. A sum of money invested at a ﬁxed rate with continuouscompounding tripled in 19 years. Find the rate. rt A = Pe 19r 3 = 1e ln 3 = 19r ln e
12. 12. A sum of money invested at a ﬁxed rate with continuouscompounding tripled in 19 years. Find the rate. rt A = Pe 19r 3 = 1e ln 3 = 19r ln e ln 3 =r 19
13. 13. A sum of money invested at a ﬁxed rate with continuouscompounding tripled in 19 years. Find the rate. rt A = Pe 19r 3 = 1e ln 3 = 19r ln e ln 3 =r 19 r ≈ 5.8%
14. 14. If I o and I denote the intensity of light before andafter going through a material, and x is the distance infeet the light travels in the material, then −1 ⎛ I ⎞ ln ⎜ ⎟ = x k ⎝ I o ⎠where k is a constant depending on the type of material.
15. 15. If I o and I denote the intensity of light before andafter going through a material, and x is the distance infeet the light travels in the material, then −1 ⎛ I ⎞ ln ⎜ ⎟ = x k ⎝ I o ⎠where k is a constant depending on the type of material. This is the Beer-Lambert Law
16. 16. If I o and I denote the intensity of light before andafter going through a material, and x is the distance infeet the light travels in the material, then −1 ⎛ I ⎞ ln ⎜ ⎟ = x k ⎝ I o ⎠where k is a constant depending on the type of material. This is the Beer-Lambert Law Solve the equation for I
17. 17. −1 ⎛ I ⎞ ln ⎜ ⎟ = xk ⎝ I o ⎠
18. 18. −1 ⎛ I ⎞ ln ⎜ ⎟ = xk ⎝ I o ⎠ ⎛ I ⎞ln ⎜ ⎟ = −kx ⎝ I o ⎠
19. 19. −1 ⎛ I ⎞ ln ⎜ ⎟ = xk ⎝ I o ⎠ ⎛ I ⎞ln ⎜ ⎟ = −kx ⎝ I o ⎠ − kx I e = Io
20. 20. −1 ⎛ I ⎞ ln ⎜ ⎟ = xk ⎝ I o ⎠ ⎛ I ⎞ln ⎜ ⎟ = −kx ⎝ I o ⎠ − kx I e = Io − kx I oe =I
21. 21. −1 ⎛ I ⎞ ln ⎜ ⎟ = xk ⎝ I o ⎠ ⎛ I ⎞ln ⎜ ⎟ = −kx ⎝ I o ⎠ − kx I e = Io − kx I oe =I or − kx I = I oe
22. 22. −1 ⎛ I ⎞ ln ⎜ ⎟ = x This is just a variation ofk ⎝ I o ⎠ rt A = Ao e ⎛ I ⎞ln ⎜ ⎟ = −kx or ⎝ I o ⎠ rt − kx I y = Pe e = Io − kx I oe =I (This is part of Example 10 or on page 364) − kx I = I oe
23. 23. HW #9It is literally true that you can succeed best andquickest by helping others to succeed. Napoleon Hill