1 / 15

Warm-Up: February 14, 2012 Solve for x

Warm-Up: February 14, 2012 Solve for x. Homework Questions?. Modeling with Exponential and Logarithmic Functions. Section 3.5. Exponential Growth and Decay. A 0 is the original amount (at t=0) A is the amount at time t k is the growth rate or decay rate k<0  Exponential decay

tobias
Download Presentation

Warm-Up: February 14, 2012 Solve for x

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. Warm-Up: February 14, 2012Solve for x

  2. Homework Questions?

  3. Modeling with Exponential and Logarithmic Functions Section 3.5

  4. Exponential Growth and Decay • A0 is the original amount (at t=0) • A is the amount at time t • k is the growth rate or decay rate • k<0  Exponential decay • k>0  Exponential growth

  5. Real World Applications • Population growth • People • Bacteria • Continuous compounding of interest • Nuclear reactions • Processing power of computers (Moore’s Law) • Half-lives of radioactive isotopes • Carbon dating • Other dating to determine ages of dinosaurs, etc. • Rate of cooling (temp.) • First order chemical reaction rates • Atmospheric pressure (as a function of height) Exponential Growth Exponential Decay

  6. Example 1: Exponential Growth • The exponential growth model describes the population of the United States, A, in millions, t years after 1970. • What was the population in 1970? • By what percentage is the population increasing each year? • When will the population be 500 million? • What does our model predict to be the population in 2011? • The US Bureau of the Census estimates there to currently be 311 million people (as of 2/9/2011). What does this say about our model?

  7. You-Try #1: Exponential Growth • The exponential growth model describes the population of India, A, in millions, t years after 1990. • What was the population in 1990? • By what percentage is the population increasing each year? • When did the population of India break 1 billion (1000 million)? • What does our model predict to be India’s population in 2011?

  8. Half-Life • The half-life of a substance (typically a radioactive isotope) is the amount of time required for half of a given sample to disintegrate. • A is the amount after time t • A0 is the original amount (at t=0) • thalf is the half-life of the substance, measured in the same units as t

  9. Example 2: Half-Lives • Carbon-14 has a half-life of 5730 years. An artifact was found that had 25 grams of carbon-14. If its original carbon-14 content was 75 grams, how old is the artifact?

  10. You-Try #2: Half-Lives • Krypton-91 has a half-life of 10 seconds. A scientist creates 12 grams of krypton-91. He needs at least 1 gram to perform a particular test on the krypton. How long does he have after creating the kryption-91 to run his test?

  11. Writing an Exponential Model • Set A0 equal to the original (earlier) amount • Use the later data to solve for k • Write the model, using the values of A0 and k

  12. Example 3: Writing a Model • According to the US Bureau of the Census, in 1990 there were 22.4 million residents of Hispanic origin living in the United States. By 2000, the number had increased to 35.3 million. • Write an exponential model for the growth of the US Hispanic population. • Use your model to estimate the current US Hispanic population.

  13. You-Try #3: Writing a Model • The 1990 population of Europe was 509 million; in 2000, it was 729 million. • Write the exponential growth function that describes the population of Europe. • Use your model to estimate the current population of Europe.

  14. Assignments • Exponential Models Worksheet – due Thursday • Chapter 3 Review – due Thursday • 10-3 Worksheet due Wednesday • Cumulative Review due Thursday

  15. Thursday’s Test • Very similar to your practice test • 21 multiple choice questions • Questions will not be in order (3.13.5) • You need to have your calculator with you. You will not be able to borrow or share. • Closed-notes (no index card)

More Related