#48. Exponential Decay Word Problem (Estimating the Age of Dinosaur Bones)

TL;DR

The video explains how to use the radioactive decay model to estimate the age of dinosaur bones through a step-by-step calculation.

Transcript

okay we have this word problem the bones of a newly discovered dinosaur weigh 170 pounds and measure nine feet wow it's big with a six-inch claw on one toe of each hind foot that says that the age of the dinosaur was estimated using a radioactive substance dating rock surrounding the bones and it wants us to complete parts a and b so let's go ahead... Read More

Key Insights

• 🛟 Radioactive substances decay exponentially with a specific half-life, reducing by half every 1.38 billion years.
• 🚟 The decay model formula, a = a sub 0 e to the kt, provides a way to calculate the remaining amount of a substance after a certain time.

Questions & Answers

Q: How does the radioactive decay model work?

The radioactive decay model states that the amount of a radioactive substance decreases by half every 1.38 billion years.

Q: How do you find the decay rate using the decay model formula?

By plugging in the fact that after 1.38 billion years, the remaining amount is half of the initial amount, we can solve for k in the formula a = a sub 0 e to the kt.

Q: What is the significance of taking the natural log of both sides in the decay model?

By taking the natural log of both sides, we can isolate k in the equation and solve for its value.

Q: How is the radioactive decay model used to estimate the age of dinosaur bones?

By analyzing the rocks surrounding the bones and determining that 94.6% of the original substance is still present, we can set a to 0.946 of the initial amount in the decay model formula and solve for t to estimate the age of the bones.

Summary & Key Takeaways

• The video discusses the radioactive decay model, which states that the radioactive substance reduces by half every 1.38 billion years.

• The formula for the decay model is given as a = a sub 0 e to the negative 0.50228 t, where a is the amount remaining after t years.

• The video demonstrates how to find the decay rate (k) by using the fact that after 1.38 billion years, the amount remaining should be half of the initial amount.