The table below shows the population of a fictional California Gold Rush Town named Lehi in the vears after its peak population in 1880. Year 1880 1890 1900 1910 1920 1930 Population 8500 5417 5674 5703 3788 2631 For the purpose of this problem, let P represent the population of Lehi t years after 1880 (t=D0 represents 1880). The new table is: 10 20 30 40 50 P(t) 8500 5417 5674 5703 3788 2631

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Exponential Regression
The table below shows the population of a fictional California Gold Rush Town named Lehi in the vegrs
after its peak population in 1880.
years
1910
1930
1920
3788
Year
1880
1890
1900
Population
8500
5417
5674
5703
2631
For the purpose of this problem, let P represent the population of Lehi t years after 1880 (t-0
represents 1880). The new table is:
10
20
30
40
50
P(t)
8500
5417
5674
5703
3788
2631
Use your calculator to determine the exponential regression equation that models the set of data above.
Round the "a" value to two decimals, and round the "b" value to two decimals. Use the indicated
variables and proper function notation.
P(t) =
Based on the your regression model, what is the percent decrease per year?
Find P(35). Round your answer to the nearest whole number.
P(35) =
Interpret your answer by completing the following sentence. Be sure to use units in your answer.
"The population of Lehi
after 1880 was about
How long did it take for the population of Lehi to reach 300 people? Round your answer to the nearest
whole number.
P(t)
300when t
=
Interpret your answer by completing the following sentence. Be sure to use units in your answer.
In
after 1880, the population of Lehi was about
How long did it take for the population of Lehi to drop by half? Round your answer to the nearest whole
number.
P(t) has halved when t =
Interpret your answer by completing the following sentence. Be sure to use units in your answer.
In
after 1880, the population of Lehi had dropped by about half.
Transcribed Image Text:Exponential Regression The table below shows the population of a fictional California Gold Rush Town named Lehi in the vegrs after its peak population in 1880. years 1910 1930 1920 3788 Year 1880 1890 1900 Population 8500 5417 5674 5703 2631 For the purpose of this problem, let P represent the population of Lehi t years after 1880 (t-0 represents 1880). The new table is: 10 20 30 40 50 P(t) 8500 5417 5674 5703 3788 2631 Use your calculator to determine the exponential regression equation that models the set of data above. Round the "a" value to two decimals, and round the "b" value to two decimals. Use the indicated variables and proper function notation. P(t) = Based on the your regression model, what is the percent decrease per year? Find P(35). Round your answer to the nearest whole number. P(35) = Interpret your answer by completing the following sentence. Be sure to use units in your answer. "The population of Lehi after 1880 was about How long did it take for the population of Lehi to reach 300 people? Round your answer to the nearest whole number. P(t) 300when t = Interpret your answer by completing the following sentence. Be sure to use units in your answer. In after 1880, the population of Lehi was about How long did it take for the population of Lehi to drop by half? Round your answer to the nearest whole number. P(t) has halved when t = Interpret your answer by completing the following sentence. Be sure to use units in your answer. In after 1880, the population of Lehi had dropped by about half.
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