1. Continually Compounded

2. Definition/Formula The natural logarithmic function can be used to solve an equation of the form for the exponent t in order to find the time it takes for an investment that is compounded continuously to reach a specific amount.

3. Example How long does it take for an investment to double at an annual amount of 8.5% compounded continuously?

4. Example How long does it take an investment to double at an annual rate of 7.5% compounded continuously?

5. Example Find the amount, A, for an investment of $1000 at an annual rate of 4% for 10 years.

6. Example How long will it take to double your money if you deposit $1200 at an annual rate of 6.9% compounded continuously?

7. Radioactive Decay The function represents the decay of carbon-14, where:

8. Example A piece of charcoal from an ancient campsite is found in an archaeological dig. It contains 9% of its original amount of carbon-14. Estimate the age of the charcoal.

9. Assignment Complete WS 4 #13-23