Exponential Functions and Population Dynamics

The video tutorial explains how to use an exponential function to model the population of a town over time. It introduces the standard form of an exponential function, highlighting the roles of the starting value and the base. The tutorial focuses on analyzing the base value to determine whether the function represents exponential growth or decay. In this case, since the base is less than one, the function indicates decay.

What is the purpose of the exponential function y = 4.5 * 0.97 ^ x in the context of the video?

• To determine the town's geographical area

• To model the population of a town over time

• To calculate the town's annual revenue

• To predict the weather patterns in the town

In the standard form of an exponential function, what does the variable 'x' represent?

• The rate of growth

• The base of the function

• The initial population

• Time in years

What does the 'a' in the exponential function y = a * B ^ x signify?

• The rate of decay

• The starting value or initial amount

• The base of the function

• The time period

What does it mean if the base 'B' in an exponential function is less than one?

• The function remains constant

• The function is undefined

• The function represents exponential decay

• The function represents exponential growth

In the function y = 4.5 * 0.97 ^ x, what does the base 0.97 indicate about the town's population?

• The population is increasing

• The population is decreasing

• The population is fluctuating

• The population is stable

If the base 'B' were greater than one, what would that imply about the town's population?

• The population is increasing

• The population is stable

• The population is undefined

• The population is decreasing