Population Growth and Exponential Decay

The video tutorial covers word problems involving natural logarithms, focusing on population growth and radioactive decay. It explains exponential growth using a population model and exponential decay using a radioactive decay model. The tutorial also provides an example of exponential growth with a mice population. The video concludes with a preview of the next topic on logarithm tables and change of base formula.

What are the two main topics discussed in the video related to natural logarithms?

• Population growth and radioactive decay

• Weather patterns and climate change

• Chemical reactions and physics

• Interest rates and inflation

Which mathematical model is used to describe population growth?

• Logarithmic model

• Quadratic model

• Linear model

• Exponential growth model

In the population growth example, what was the initial population of the United States in 1970?

• 247 million

• 203 million

• 150 million

• 300 million

What is the purpose of calculating the constant K in the population growth model?

• To calculate the birth rate

• To find the death rate

• To predict future population

• To determine the initial population

How do you solve for K using natural logarithms?

• By multiplying both sides by K

• By adding K to both sides

• By dividing both sides by K

• By taking the natural logarithm of both sides

What is the estimated population of the USA in 2020 according to the model?

• 340 million

• 300 million

• 400 million

• 250 million

What is radioactive decay an example of?

• Linear decay

• Exponential decay

• Quadratic decay

• Logarithmic decay

What is the half-life of strontium 90?

• 100 years

• 25 years

• 10 years

• 50 years

How is the decay constant K calculated for a radioactive substance?

• By subtracting the half-life from the initial amount

• By adding the half-life to the initial amount

• By dividing the natural log of 0.5 by the half-life

• By multiplying the half-life by 2

After 100 years, how much of a 36g sample of strontium 90 remains?

• 10g

• 18g

• 2.26g

• 5g