Exponential Regression
The table below shows the population of a fictional California Gold Rush Town named Lehi in the years after
its peak population in 1880.
Year
1880 1890 1900 1910 1920 1930
Population 9100 3823 2639 1748 765 350
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:
P 9100 3823 2639 1748 765 350
P(t)
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 270 people? Round your answer to the nearest whole
number.
P(t)=270 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 was about
How long did it take for the population of Lehi to drop by half? Round your answer to the nearest whole
number.
Use the initial population in the model (not the initial value in the table).
P(t) has halved when t =