Half-Life and Exponential Decay Concepts

The video tutorial explains how to determine the half-life of a radioactive substance using an exponential decay model. It starts with a scientist having 200 grams of radioactive goo, which decays to 15.2 grams after 40 minutes. The tutorial derives the exponential decay formula, calculates the continuous decay rate, and uses it to find the half-life and the remaining amount after 71 minutes. The half-life is approximately 10.8 minutes, and about 2.1 grams remain after 71 minutes.

What is the initial amount of radioactive goo the scientist starts with?

• 71 grams

• 200 grams

• 100 grams

• 15.2 grams

After how many minutes does the sample decay to 15.2 grams?

• 50 minutes

• 20 minutes

• 30 minutes

• 40 minutes

Which form of the exponential function is used in this example?

• Fourth form

• First form

• Second form

• Third form

What is the continuous decay rate (K) rounded to six decimal places?

• -0.064246

• -0.046426

• -0.046246

• -0.064426

What is the first step in solving for the decay rate K?

• Add 200 to both sides

• Divide both sides by 200

• Subtract 200 from both sides

• Multiply both sides by 200

What is the approximate half-life of the radioactive goo in minutes?

• 8.5 minutes

• 11.8 minutes

• 9.8 minutes

• 10.8 minutes

What is the shortcut formula for determining the half-life using the decay rate?

• Natural log of 2/1 divided by K

• Natural log of 1 divided by K

• Natural log of 2 divided by K

• Natural log of 1/2 divided by K

How many grams of goo remain after 71 minutes?

• 1.1 grams

• 2.1 grams

• 3.1 grams

• 4.1 grams

What is the formula used to determine the amount of goo after time T?

• P(T) = 200 x E^(-0.064426 x T)

• P(T) = 100 x E^(-0.064426 x T)

• P(T) = 200 x E^(0.064426 x T)

• P(T) = 100 x E^(0.064426 x T)

What is the purpose of taking the natural log of both sides of the equation?

• To simplify the equation

• To solve for T

• To solve for K

• To find the initial amount