The video tutorial covers the application of first-order differential equations, focusing on growth and decay laws. It explains the mathematical formulation and provides step-by-step solutions to problems involving radium decay and population growth. The tutorial also includes calculations for half-life and long-term decay analysis, offering a comprehensive understanding of how differential equations can model real-world scenarios.

What is the primary focus of the video tutorial?

• Application of second-order differential equations

• Application of calculus in physics

• Application of first-order differential equations

• Application of algebraic equations

What does the rate of change in growth and decay depend on?

• The initial amount of substance

• The quantity of substance present at any time

• The temperature of the environment

• The pressure applied to the substance

What is the general solution for the differential equation discussed?

• X = C * e^(KT)

• X = C * e^(KT) + D

• X = C * e^(KT) - D

• X = C * e^(KT) / D

In the radium decay example, what is the initial amount of radium?

• 20 grams

• 40 grams

• 30 grams

• 10 grams

How is the value of K determined in the radium decay problem?

• By using both the initial amount and the amount after a certain time

• By using the temperature of the environment

• By using the amount after a certain time

• By using the initial amount only

What is the half-life of radium in the example problem?

• 1300.25 years

• 1200.50 years

• 1400.00 years

• 1151.78 years

After 900 years, how much radium remains?

• 11.63 grams

• 12.00 grams

• 13.50 grams

• 14.00 grams

In the new decay problem, what is assumed as the initial amount?

• 100 grams

• 75 grams

• 150 grams

• 50 grams

How long does it take for half of the original amount to decompose in the new problem?

• 1700.50 years

• 1600.00 years

• 1566.65 years

• 1800.75 years

What percentage of the substance decomposes in 50 years?

• 3.00%

• 4.50%

• 5.00%

• 2.19%