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.)
____ %

1. 👍
2. 👎
3. 👁
1. 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.

1. 👍
2. 👎

## Similar Questions

1. ### Algebra

In 2006 population of country was 32.2 million. This represented an increase of 3.6% since 2001. What was population of country in 2001. Round to nearest hundredth of a million.

2. ### Math

Teaneck High had an enrollment of 11040 in 1985 and an enrollment of 12100 in year 1998. What is the predicted enrollment of Teaneck High in 2014 if we assume a linear model?

3. ### Calculus - Integrals

The projected rate of increase in enrollment at a new college is estimated by dE/dt = 6,000(t+1)^-3/2 where E(t) is the projected enrollment in t years. If the enrollment is 3,000 now (t=0), find the projected enrollment 15 years

4. ### algebra 2

Teaneck High had an enrollment of 11050 in 1990 and an enrollment of 13390 in year 1998. What is the predicted enrollment of Teaneck High in 2018 if we assume a linear model?

1. ### STATISTICS

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned

2. ### calculus

The population of a country was 8.4 million people in 2000. Three years later, the population of the same nation was 9.3 million people. Assuming that population is growing exponentially, what is the projected population (rounded

3. ### Algebra 2

A country's population in 1991 was 15 million. In 2001 it was 16 million. Estimate the population in 2005 using exponential growth formula. Round your answer to the nearest million.

4. ### Finance

Following are selected balance sheet accounts for Third State Bank: vault cash  \$2 million; U.S. government securities  \$5 million; demand deposits  \$13 million; nontransactional accounts  \$20 million; cash items in process of

1. ### statistic

1. Compute descriptive statistics for liberal art colleges and research universities in the Excel file colleges and universities. Compare the two types of colleges . what can you conclude.? 2.The Excel file MBA Student survey

2. ### algebra

A country's population in 1995 was 175 million. In 2000 it was 181 million. Estimate the population in 2020 using the exponential growth formula. Round you answer to the nearest million. P=Ae^kt

3. ### math

the number of students at a university increases from 8000 in 1970 to 20,000 in 2000. what was the percent increase in enrollment from 1970 to 2000?

4. ### math

XYZ Oil Company has consistently lost \$8 million each year for the past 7 years. Express the total loss as an integer. A) \$8 million B) -\$8 million C) \$48 million D) -\$56 million