Here you will compare the population growth of Bentonville, AR to the population decay of Pine Bluff, AR.
In 2000, the population of Bentonville was 20,308 people and Pine Bluff's was 55,068 people.
The population growth rate for Bentonville since 2000 is 5.07%
The population decay rate for Pine Bluff since 2000 is 1.43%
Question 1
Write an exponential function to represent the Bentonville’s population, y, based on the number of years after 2000, x, after a period of exponential growth.(1 point)
The exponential function to represent Bentonville's population, y, based on the number of years after 2000, x, after a period of exponential growth is:
y = 20,308 * (1 + 0.0507)^x
Write an exponential function to represent the Pine Bluff’s population, y, based on the number of years after 2000, x, after a period of population decline.(1 point)
The exponential function to represent Pine Bluff's population, y, based on the number of years after 2000, x, after a period of population decline is:
y = 55,068 * (1 - 0.0143)^x
Explain the similarities and differences between your equations for Bentonville and Pine Bluff.
The similarity between the equations for Bentonville and Pine Bluff is that both are exponential functions that represent the population change over time. They both have a base growth rate (1 + growth rate) and a base decay rate (1 - decay rate) that determines the rate at which the population increases or decreases.
The difference between the equations is in the values of the growth and decay rates. For Bentonville, the growth rate is 5.07% (0.0507), indicating a positive growth in population over time. On the other hand, Pine Bluff has a decay rate of 1.43% (0.0143), indicating a negative population growth or decline over time.
Additionally, the initial population values for Bentonville (20,308) and Pine Bluff (55,068) are different, reflecting the different starting populations of the two cities in 2000.
simplify
To simplify the equations, we can express the growth and decay rates as decimal values.
For Bentonville:
y = 20,308 * (1 + 0.0507)^x
Simplified: y = 20,308 * 1.0507^x
For Pine Bluff:
y = 55,068 * (1 - 0.0143)^x
Simplified: y = 55,068 * 0.9857^x
graph this
To graph these exponential functions, we can plot the population (y) on the y-axis and the number of years after 2000 (x) on the x-axis.
For Bentonville:
y = 20,308 * 1.0507^x
For Pine Bluff:
y = 55,068 * 0.9857^x
Here is the graph:
[Graph image cannot be generated without specific values for x-axis]