Part A:
For the town population data, the curve of best fit appears to be an exponential function of the form y = ab^x. Using the graphing tool, we can estimate the values of a and b to be:
a = 5.98
b = 1.121
Therefore, the equation of the curve of best fit is y = 5.98(1.121)^x.
For the bee population data, the curve of best fit also appears to be an exponential function of the form y = ab^x. Using the graphing tool, we can estimate the values of a and b to be:
a = 321.38
b = 0.675
Therefore, the equation of the curve of best fit is y = 321.38(0.675)^x.
Part B:
To find the population of the town 25 years after the council started tracking the population data, we can substitute x = 25 into the equation of the curve of best fit for the town population data:
y = 5.98(1.121)^25 ≈ 572,400
Therefore, the estimated population of the town 25 years after the council started tracking the population data is approximately 572,400 people.
For the bee population data, we can use the equation of the curve of best fit to predict the bee population in the 12th year after initially recording the data, which corresponds to x = 12.y = 321.38(0.675)^12 ≈ 2.92
Therefore, the estimated bee population in the 12th year after initially recording the data is approximately 2,920 bees (rounded to the nearest whole number).
Since the town council has set a threshold of 5,000 bees before taking action to support the bee population, it appears that the agricultural committee will not have a good chance of convincing the board to support bees this time around. The estimated bee population is well below the threshold set by the council, and it would take several years of significant growth for the bee population to reach that level. Therefore, the committee would need to provide strong evidence of the importance of bees to the ecosystem and the potential consequences of not taking action to support them in order to convince the board to change their stance.