Based on the given data, we can see that the number of visitors to the park does not increase or decrease in a consistent pattern as the temperature increases. This suggests that a linear model is not appropriate. Additionally, the number of visitors does not increase at a constant rate as the temperature increases, ruling out a quadratic model.
Therefore, an exponential model is most appropriate for modeling the relationship between temperature and the number of visitors. As the temperature increases, the number of visitors grows at an increasing rate, which is characteristic of exponential growth.
Using a graphing utility, we can define the exponential function f(t) = a*b^t, where t is the daily high temperature in degrees Fahrenheit. Using the data points provided, we can determine the values of a and b in the function.
Using the model, we can determine the predicted number of visitors when the daily high temperature is 68°F. By plugging in t = 68 into the exponential function and solving for f(t), we can find the predicted number of visitors.
Temperature (°F)
50
55
60
65
70
75
80
85
90
95
100
Number of visitors
420
637
824
1,185
1,210
1,232
1,156
845
658
315
256
A park ranger is investigating the relationship between the outside temperature and the number of visitors to the park. The table gives recorded daily high temperatures, in degrees Fahrenheit (°F), and the corresponding number of visitors to the park for selected days.
The function f models the number of visitors in terms of daily high temperature t, in degrees Fahrenheit (° F), on the interval 50 ≤ t ≤ 100.
• Use the table of values to determine if a linear, quadratic, or exponential function model is most appropriate for f.
Give a reason for your answer.
• Use a graphing utility to define f based on your chosen function model.
• Using the model, determine the predicted number of visitors when the daily high temperature is 68° F.
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