Download presentation

Presentation is loading. Please wait.

Published byCole O'Connell Modified over 3 years ago

1
The Natural Base, e Objective: Model exponential growth/decay.

5
The Natural Exponential Function

7
Example 1

11
Example 2

13
Try This Find the value of $500 after 4 years invested at an annual interest rate of 9% compounded monthly and continuously.

14
Try This Find the value of $500 after 4 years invested at an annual interest rate of 9% compounded monthly and continuously.

15
Try This Find the value of $500 after 4 years invested at an annual interest rate of 9% compounded monthly and continuously.

17
Example 3

20
Inverse Functions Remember, lnx and e x are inverse functions. This means that:

21
Example 4

23
Try This How long does it take for an investment to triple at an annual interest rate of 7.2% compounded continuously?

24
Try This How long does it take for an investment to triple at an annual interest rate of 7.2% compounded continuously?

25
Try This How long does it take for an investment to triple at an annual interest rate of 7.2% compounded continuously?

26
Radioactive Decay Most of the carbon found in the Earths atmosphere is the isotope cardon-12, but a small amount is the radioactive isotope carbon-14. Plants absorb carbon dioxide from the atmosphere, and animals obtain carbon from the plants they consume. When a plant or animal dies, the amount of carbon-14 it contains decays in such a way that exactly half of its initial amount is present after 5730 years. The function below models the decay of carbon-14.

27
Example 5 Suppose that archaeologists find scrolls and claim that they are 2000 years old. Tests indicate that the scrolls contain 78% of their original carbon-14.

28
Example 5 Suppose that archaeologists find scrolls and claim that they are 2000 years old. Tests indicate that the scrolls contain 78% of their original carbon-14. Could the scrolls be 2000 years old?

29
Example 5 Suppose that archaeologists find scrolls and claim that they are 2000 years old. Tests indicate that the scrolls contain 78% of their original carbon-14. Could the scrolls be 2000 years old?

30
Example 5 Suppose that archaeologists find scrolls and claim that they are 2000 years old. Tests indicate that the scrolls contain 78% of their original carbon-14. Could the scrolls be 2000 years old?

32
Homework Pages 397-399 13-59 odd 75,77,79

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google