1 / 13

Exploring Natural Logarithms and Exponential Functions

Learn about the inverse relationship between y=ex and y=ln(x), using natural logs to solve equations, graphing functions, and calculating values with base "e". Practice examples included.

eowen
Download Presentation

Exploring Natural Logarithms and Exponential Functions

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. Natural Logarithms

  2. Natural Logs and“e” The function y=ex has an inverse called the Natural Logarithmic Function. Start by graphing y=ex Y=ln x

  3. What do you notice about the graphs of y=ex and y=ln x? y=ex and y=ln x are inverses of each other! We can use the natural log to “undo” the function y= ex (and vice versa).

  4. All the rules still apply • You can use your product, power and quotient rules for natural logs just like you do for regular logs Let’s try one:

  5. Solving with base “e” 1. Subtract 2.5 from both sides 2. Divide both sides by 7 3. Take the natural log of both sides. 4. Simplify. 5. Divide both sides by 2 x = 0.458 6. Calculator

  6. Another Example: Solving with base “e” 1. Take the natural log of both sides. 2. Simplify. 3. Subtract 1 from both sides x = 2.401 4. Calculator

  7. Solving a Natural Log problem To “undo” a natural log, we use “e” 1. Rewrite in exponential form 2. Use a calculator 3. Simplify.

  8. Another Example: Solving Natural Logs 1. Rewrite in exponential form. 2. Calculator. 3. Take the square root of each time 3x+5 = 7.39 or -7.39 4. Calculator X=0.797 or -4.130 5. Simplify

  9. Let’s try some

  10. Let’s try some

  11. Going back to our continuously compounding interest problems . . . A $20,000 investment appreciates 10% each year. How long until the stock is worth $50,000? Remember our base formula is A = Pert . . . We now have the ability to solve for t A = $50,000 (how much the car will be worth after the depreciation) P = $20,000 (initial value) r = 0.10 t = time From what we have learned, try solving for time

  12. Going back to our continuously compounding interest problems . . . $20,000 appreciates 10% each year. How long until the stock is worth $50,000? A = $50,000 (how much the car will be worth after the depreciation) P = $20,000 (initial value) r = 0.10 t = time

  13. Special Thanks to: • Pleasanton, CA Public Schools • www.pleasanton.k12.ca.us/.../Powerpoints/.../8.6%20Natural%...

More Related