Carbon-14 Decay and Exponential Functions

The video tutorial covers various topics related to exponential functions and decay. It begins with calculating the half-life of carbon-14 in fossils and estimating the age of a tree fossil. It then formulates a decay function for nickel-63 and analyzes exponential growth functions. The tutorial also models city population growth over decades and graphs exponential functions to find specific values. Finally, it identifies equivalent expressions for powers, providing a comprehensive understanding of exponential concepts.

What is the half-life of Carbon-14?

• 5,730 years

• 100 years

• 10,000 years

• 1,000 years

If a fossil has 6 picograms of Carbon-14, what is the initial value in the decay equation?

• 3 picograms

• 1 picogram

• 12 picograms

• 6 picograms

How often does the half-life of Carbon-14 occur?

• Every 10,000 years

• Every 5,730 years

• Every 1,000 years

• Every 100 years

How many half-lives have passed if a tree fossil's Carbon-14 level is reduced to 0.5 picograms from 4.2 picograms?

• One half-life

• Four half-lives

• Two half-lives

• Three half-lives

What is the total time in years for three half-lives of Carbon-14?

• 5,730 years

• 22,920 years

• 17,190 years

• 11,460 years

What is the half-life of Nickel-63?

• 100 years

• 500 years

• 50 years

• 200 years

How many days are there in 100 years?

• 36,500 days

• 30,000 days

• 40,000 days

• 50,000 days

What is the growth factor for the function f(x) = 5^x over an interval of 1/10?

• 5

• Cube root of 5

• 10th root of 5

• Square root of 5

What is the growth rate of the population modeled by the equation with a base of 1.3?

• 10%

• 20%

• 30%

• 40%

What does the initial value of 100,000 represent in the population model?

• Initial century

• Initial population

• Initial growth rate

• Initial decade