Carbon-14 Decay and Exponential Functions

This video tutorial covers exponential functions with base e, focusing on growth and decay. It provides a detailed example using carbon-14 decay, demonstrating how to model the decay process with an exponential function. The tutorial includes calculations to determine the remaining carbon-14 after 120 years and the age of an artifact with a given amount of carbon-14. Both graphical and algebraic methods are used to solve the problems, with a focus on using logarithms for algebraic solutions.

What is the general form of an exponential function with base e?

• f(x) = a * k^x

• f(x) = a * e^(kx)

• f(x) = a * x^k

• f(x) = a * e^(x/k)

In an exponential function with base e, what does a negative k value indicate?

• Exponential growth

• Linear decay

• Exponential decay

• Linear growth

What is the initial amount of carbon-14 in the given problem?

• 15 grams

• 20 grams

• 50 grams

• 100 grams

How is the continuous decay rate expressed as a decimal in the problem?

• -0.012097

• -0.00012097

• 0.012097

• 0.00012097

After 120 years, approximately how much carbon-14 remains?

• 49.279 grams

• 20 grams

• 50 grams

• 30 grams

What is the purpose of using a graphing calculator in the problem?

• To find the initial amount

• To determine the point of intersection

• To calculate the decay rate

• To convert percentages to decimals

What is the approximate age of the artifact if 20 grams of carbon-14 remain?

• 5000 years

• 7574.53 years

• 2000 years

• 10000 years

Which logarithm is used to solve the equation algebraically?

• Common logarithm

• Natural logarithm

• Binary logarithm

• Decimal logarithm

What is the first step in solving the equation algebraically?

• Add 50 to both sides

• Subtract 50 from both sides

• Divide both sides by 50

• Multiply both sides by 50

What is the final step in solving for t using logarithms?

• Add the coefficient

• Multiply by the coefficient

• Subtract the coefficient

• Divide by the coefficient