Saturday

April 19, 2014

April 19, 2014

Posted by **jam** on Saturday, May 18, 2013 at 7:22pm.

(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 -
**MathMate**, Sunday, May 19, 2013 at 1:37pmLet 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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