Exponential Data
In this activity, you will graph and write exponential functions to model population data presented in tables. Then you’ll use your models to make predictions and draw a conclusion.

Question 1
A town’s population has been exponentially increasing for the past 10 years. The town council initially recorded the town’s population at 6,000 people and tracked it each year after that. The table represents their data.

Years Town Population
(in thousands)
0 6
1 6.9
2 9
3 10.5
4 13
5 14.2
6 18
7 20.8
8 26
9 31.3
Use the graphing tool to plot the population data and determine the curve of best fit.

Part A
Question
What is the equation of the curve of best fit for the population data?

Enter the correct answer in the box by replacing a and b with the values from the graphing tool. Do not round the values of a and b.

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Part B
Question
If the town continues to grow at the same rate, approximately what will be the population, to the nearest 100 people, 25 years after the town council started tracking the population data?

341,100 people
180,000 people
271,200 people
572,400 people
Question 2
Because of the growth in the town’s population, the agricultural department kept track of the town’s native bee population during the same time period. They feared with the increase of people in the town, the bee population would start to decrease, affecting the ecosystem. Their data is shown in the table.

Years Bee Population
(in thousands)
0 320
1 225
2 152.6
3 111.2
4 75
5 56.8
6 36.7
7 26.9
8 17.5
9 13.2
Use the graphing tool to plot the population data and determine the curve of best fit.

Part A
Question
What is the equation of the curve of best fit for the population data?

Enter the correct answer in the box by replacing a and b with the values from the graphing tool. Do not round the values of a and b.

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Part B
After several years of recording the data, the agricultural committee requested help from the town council for a grant to boost the bee population. The council denied the request, saying it wouldn’t take any action until the population dropped below 5,000 bees.

In the 12th year after initially recording the bee population, the agricultural committee plans to speak with the board again. Will the committee have a good chance of convincing the board to help support bees this time around? Justify your conclusion using mathematical reasoning.