Modeling exponential functions for the decrease of a population

The video tutorial covers exponential and modeling equations, explaining their components and application. The teacher demonstrates solving a problem using these equations, highlighting common mistakes and corrections. The focus is on understanding the equation's variables and applying them correctly to find the solution.

What does the variable 'a' represent in the equation a(t) = a * (1 + r)^t?

• The time period

• The amount after time t

• The initial amount

• The rate of change

In the context of the problem discussed, what is the initial population?

• 752,000

• 18 years

• 58,000

• 1.4%

How should the rate be expressed when dealing with a decrease in population?

• As a positive decimal

• As a fraction

• As a percentage

• As a negative decimal

What is the correct rate to use for a 1.4% decrease?

• 0.986

• 1.014

• 0.014

• 1.4

What is the final population after applying the corrected formula?

• 752,000

• 58,000

• 583,448

• 500,000

Why is it important to verify the results of a calculation logically?

• To ensure the numbers are large

• To confirm the calculation is correct

• To avoid using a calculator

• To make the process faster

What mistake did the teacher initially make in the calculation?

• Added instead of subtracting the rate

• Multiplied before using the exponent

• Forgot to convert the rate to a decimal

• Used the wrong initial population