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In 1970, the total enrollment in public universities and colleges in a country was 5.1 million students. By 2004, enrollment had risen to 14.3 million students. Assume enrollment can be modeled by exponential growth.

(a) Estimate the total enrollments in 1980, 1990, and 2000. (Round your answers to one decimal place.)

1980___ million
1990___ million
2000___ million

(b) How many years after 1970 until the enrollment doubles from the 2004 figure? (Round your answer to one decimal place.)
____ years

(c) By what percent is the enrollment increasing each year? (Round your answer to two decimal places.)
____ %

• Exponential modelling -

Let the mathematical model be

f(x)=ax^b
where x=years past 1970.
f(x)=population in millions
Note: much better accuracy is obtained by shifting the origin to 1970, the closest possible.

Substituting given data for 1970:
5.1=ax^0=a
so
f(x)=5.1x^b
For 2004,
14.3=5.1(34^(b))
or
b=log(14.3/5.1)/log(34)
=.292374812

The complete model is then

f(x)=5.1x^0.292374812

Substitute x=(1980-1970)=10
to find the estimated population for 1980, etc.

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