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.
|
|
|
