1 / 9

9.5 Exponential Equations & Inequalities

9.5 Exponential Equations & Inequalities. Logarithmic vocabulary Consider: log 260 Also: log 0.26 Ex 1) Underline the mantissa & circle the characteristic log 425 = 2.6284 If we are given log x or ln x , we can find x using our calculators.

vittorio-poyntz
Download Presentation

9.5 Exponential Equations & Inequalities

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 9.5 Exponential Equations & Inequalities

  2. Logarithmic vocabulary Consider: log 260 Also: log 0.26 Ex 1) Underline the mantissa & circle the characteristic log 425 = 2.6284 If we are given log x or lnx, we can find x using our calculators. We will use 10x or ex. Let’s practice some simple ones…get those calculators ready! = 2.4150 = log (2.6 × 102) = log 2.6 + log 102 = 0.4150 + 2 = –0.5850 = log (2.6 × 10–1) = log 2.6 + log 10–1 = 0.4150 + –1 mantissa characteristic

  3. Ex 2) Solve for x to the nearest hundredth. • a) log x = 3.2274 c) lnx – 3 = 5.7213 lnx = 8.7213 e8.7213 = x 6132.15 = x 2 log x = 2.6419 log x = 1.32095 101.32095 = x 20.94 = x 103.2274 = x 1688.11 = x • To solve an exponential equation: • Isolate the exponential expression • Take the logarithm of both sides of the equation • Verify all answers! (by substitution in original)

  4. Ex 3) Solve for x to nearest hundredth. 42x – 1 – 27 = 0 42x – 1 = 27 log 42x – 1 = log 27 (2x – 1) log 4 = log 27 2x log 4 – log 4 = log 27 2x log 4 = log 27 + log 4 log 27 + log 4 2 log 4 x = 1.69 Ex 4) x =

  5. Sometimes we can’t solve algebraically, so we go to our graphing calculator. Solve using a graphing calculator. Ex 5) ex = x2 – 1 Y1 = ex Y2 = x2 – 1 (Find intersection) x = –1.15 Ex 6) y ≥ ex – 2 Y1 = ex – 2

  6. Applications Compound Interest Formula: A = total value of investment t = number of years P = principal amount invested r = interest rate n = number of times per year interest is compounded (%  decimal)

  7. Ex 7) The Smith Family wants to give their youngest daughter $20,000 when she is ready for college. They now have $11,500 to invest. Determine how many years it will take them to achieve their goal given that they invest this amount at 8.3% compounded monthly. A = 20,000 P = 11,500 r = .083 n = 12 *Watch those parentheses! t = 7 years

  8. Continuous Compound Interest Formula A = Pert Ex 8) A sum of money invested at a fixed interest rate, compounded continuously, tripled in 19 years. Determine the interest rate at which the money was invested. *you don’t know A or P but you don’t need it! You need P to triple A = Pert 3P = Per(19) P P 3 = e19r ln 3 = 19rlne ln 3 19 = r r = 5.8%

  9. Homework #906 Pg 472 #1, 3, 5, 9, 13, 18, 20–23, 25, 27, 29, 32, 33, 36, 38, 39–47 odd

More Related