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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.)
____ %

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.)
____ %
No one has answered this question yet.

To estimate the total enrollments in 1980, 1990, and 2000, we'll need to use the exponential growth model.

The general formula for exponential growth is A = P(1 + r)^t, where A is the final amount, P is the initial amount, r is the growth rate, and t is the time in years.

In this case, we have the final amount A and the initial amount P, and we're looking to find the time t.

(a)

To estimate the total enrollment in 1980:
The time difference between 1970 and 1980 is 10 years.

We can calculate the growth rate r using the formula:
r = (A/P)^(1/t) - 1

Plugging in the values:
r = (14.3/5.1)^(1/10) - 1

Calculating this value:
r = 0.0777

Now we can estimate the enrollment in 1980:
A_1980 = P(1 + r)^t
A_1980 = 5.1(1 + 0.0777)^10

Calculating this value:
A_1980 ≈ 8.9 million

So, the estimated total enrollment in 1980 is 8.9 million.

To estimate the total enrollment in 1990:
The time difference between 1970 and 1990 is 20 years.

We can use the same formula to calculate the growth rate r:
r = (14.3/5.1)^(1/20) - 1

Calculating this value:
r = 0.0427

Now we can estimate the enrollment in 1990:
A_1990 = P(1 + r)^t
A_1990 ≈ 5.1(1 + 0.0427)^20

Calculating this value:
A_1990 ≈ 11.4 million

So, the estimated total enrollment in 1990 is 11.4 million.

To estimate the total enrollment in 2000:
The time difference between 1970 and 2000 is 30 years.

Calculating the growth rate r:
r = (14.3/5.1)^(1/30) - 1

Calculating this value:
r = 0.0312

Now we can estimate the enrollment in 2000:
A_2000 = P(1 + r)^t
A_2000 ≈ 5.1(1 + 0.0312)^30

Calculating this value:
A_2000 ≈ 12.3 million

So, the estimated total enrollment in 2000 is 12.3 million.

(b)

To find out how many years after 1970 it takes for the enrollment to double from the 2004 figure, we can use the formula:

t = log2(A/P) / log2(1 + r)

Plugging in the values:
t = log2(14.3/5.1) / log2(1 + r)

Calculating this value:
t ≈ 7.2 years

So, it takes approximately 7.2 years for the enrollment to double from the 2004 figure.

(c)

To calculate the percent by which the enrollment is increasing each year, we can use the formula:

Percent increase = r * 100

Plugging in the value of r from before:
Percent increase = 0.0312 * 100

Calculating this value:
Percent increase ≈ 3.12%

So, the enrollment is increasing by approximately 3.12% each year.