Understanding Continuous Compounding with Examples and Applications
This resource explores the concept of continuous compounding, providing definitions and formulas used to calculate the time required for an investment to reach a certain amount when compounded continuously. It includes several practical examples, such as determining how long it takes to double an investment at various interest rates and calculating the future value of a given investment over time. Additionally, the document touches on radioactive decay, specifically using the decay of carbon-14 to estimate the age of archaeological findings.
Understanding Continuous Compounding with Examples and Applications
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Presentation Transcript
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.
Example How long does it take for an investment to double at an annual amount of 8.5% compounded continuously?
Example How long does it take an investment to double at an annual rate of 7.5% compounded continuously?
Example Find the amount, A, for an investment of $1000 at an annual rate of 4% for 10 years.
Example How long will it take to double your money if you deposit $1200 at an annual rate of 6.9% compounded continuously?
Radioactive Decay The function represents the decay of carbon-14, where:
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.
Assignment Complete WS 4 #13-23
