Explain the similarities and differences between your equations for Bentonville and Pine Bluff.(2 points)
Bentonville : 20308*(1+0.0507)^X
Pine Bluff : y=a*e^(kx)
The first equation for Bentonville, 20308*(1+0.0507)^X, represents exponential growth where X denotes the number of time periods and 0.0507 represents the growth rate. The equation is used to calculate the population of Bentonville over time.
The second equation for Pine Bluff, y=a*e^(kx), also represents exponential growth where x denotes the number of time periods. However, instead of a fixed growth rate, it uses the variable k to represent the growth rate. The equation is used to calculate the population of Pine Bluff over time.
Similarities:
1. Both equations represent exponential growth over time.
2. Both equations can be used to calculate the populations of their respective cities.
Differences:
1. The equation for Bentonville uses a fixed growth rate (0.0507) whereas the equation for Pine Bluff uses a variable growth rate (k).
2. The specific values in the equations differ - Bentonville's equation multiplies the initial population by (1+0.0507) raised to the power of X, while Pine Bluff's equation multiplies the initial population by e (Euler's number) raised to the power of kx.