Exponential Population Dynamics

The video tutorial explains how to use the exponential function y = 4.5 * 0.97 ^ x to model the population of a town over time. It discusses the role of the base in determining growth or decay, highlighting that a base less than one indicates a decrease. The tutorial calculates the rate of change as a 3% decrease, providing a clear understanding of exponential decay in this context.

What does the variable 'x' represent in the exponential function modeling the town's population?

• The initial population of the town

• The number of years

• The growth rate

• The base of the exponential function

What is the initial value 'a' in the exponential function y = a * b ^ x?

• The rate of decay

• The number of years

• The initial population in thousands

• The base of the function

In the exponential form y = a * b ^ x, what does the base 'b' indicate?

• The constant factor

• The time period

• The rate of change

• The initial value

What happens to the population when the base 'b' is less than one?

• The population decreases

• The population increases

• The population doubles

• The population remains constant

What would be the effect on the population if the base 'b' was exactly 1?

• The population would decrease

• The population would increase

• The population would fluctuate

• The population would remain constant

If the base 'b' is 0.97, what is the percentage change in the population each year?

• 3% decrease

• 0.03% increase

• 0.97% decrease

• 3% increase

How is the change in population calculated when the base is less than one?

• By adding the base to one

• By subtracting the base from one

• By dividing the base by the initial value

• By multiplying the base by 100

Why is the population model considered exponential?

• Because it remains constant over time

• Because it changes by a constant percentage

• Because it decreases at a constant rate

• Because it increases linearly