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.

Year188018901900191011930
Population810046594404399578571501


For the purpose of this problem, let P\displaystyle {P} represent the population of Lehi t\displaystyle {t} years after 1880 (t=0 represents 1880). The new table is:

t0102030150
P(t)810046594404399578571501
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 three decimals. Use the indicated variables and proper function notation.

P(t)=\displaystyle {P}{\left({t}\right)}=  
Based on the your regression model, what is the percent decrease per year?

%
Find P(6). Round your answer to the nearest whole number.

P(6)=\displaystyle {P}{\left({6}\right)}=

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 370 people? Round your answer to the nearest whole number.

P(t)=370\displaystyle {P}{\left({t}\right)}={370} when t=\displaystyle {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)\displaystyle {P}{\left({t}\right)} has halved when t=\displaystyle {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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