SOLUTION: The population of Collin county, which follows the exponential growth model, increased from 491,272 in 2000 to 782,341 in 2010. a. find the exponential growth rate, k. (let t=0

Question 1129809: The population of Collin county, which follows the exponential growth model, increased from 491,272 in 2000 to 782,341 in 2010.
a. find the exponential growth rate, k. (let t=0 for year 2000) round to nearest four decimal.
b. white the exponential growth function.
c. what should the population have been in 2012?
d. when should the population be 1,245,863?
e. how long did it take population to double from what it was in 2000?
f. in 2017 population was 969,603. how does this compare with our model in part b? given this result what can you say about the growth of Collin county now?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
p=ak^t
p1=491272*k^0
p2=782341*k^10
782341/491272 = k^10
k=1.047629
growth rate is 4.7629%
2012: predicted population is 491272*1.047629^12=858,642 people
1245863=491272*1.047629^t
1.047629^k=2.5363599
ln both sides is k ln 1.0476=ln 2.5363
t=20.000 years.
Rule of 72 would say 72/4.76 or 15.12 years for doubling
14.90 years
2017 predicted is 491272*1.0476^17 or 1083552, or more than actual, so the rate of growth is slowing down.

RELATED QUESTIONS
The population of Dallas County, which follows the exponential growth model, increaed... (answered by jorel1380)

Model exponential growth and decay... In 2000, the population of Israel was... (answered by Boreal)

In 2000, the population of Israel was approximately 6.04 million and by 2050 it is... (answered by stanbon)

A. In 2000, the population of a country was approximately 5.85 million and by 2015 it is... (answered by josgarithmetic)

In 1990, the population of Africa was 643 million and by 2000 it had grown to 813... (answered by stanbon)

From 1990 to 2000, the population of Texas increased from 16,985 to 20,851,820. If the... (answered by checkley71)

a.a. In 2000, the population of a country was approximately 6.27 million and by 2097it... (answered by josgarithmetic)

a. In 2000, the population of a country was approximately 6.18 million and by 2069 it... (answered by josgarithmetic)

The population of the world in 1987 was about 5 billion, and the relative growth rate was (answered by josgarithmetic)