SOLUTION: Assume that the population of the United States is increasing exponentially with time. The 1970 census showed that the population was about 203 million. the 1980 census showed that

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Question 175493: Assume that the population of the United States is increasing exponentially with time. The 1970 census showed that the population was about 203 million. the 1980 census showed that the population had grown to about 226 million.
a. Find the particular equation expressing population in terms of the number of years that have elapsed since 1970.
b. Use your equation to predict the population this year.
c. Predict the year in which the population will reach 400 million.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!

we have a 10 year span from 1970 to 1980 and the difference in population between those years was 226mil-203mil=23mil. Therefore the population is growing at 2.3mil per year(23mil/10).
:
all numbers in millions
:
A)so our highlight%28P%28t%29=2.3t%2B2.03%29
:
B)population in 2009
:
highlight%28P%2839%29=2.3%2839%29%2B203=89.7%2B203=292.7%29(million)
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C)400=2.3t+203
:
2.3t=400-203
:
2.3t=197
:
highlight%28t=85.65%29 which means between the 85 and 86 years the population will reach 400million