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

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

The Natural Exponential Function

Example 1

Example 2

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

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

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

Example 3

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

Example 4

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

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

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

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.

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.

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?

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?

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?

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