# Math

posted by .

According to the U.S Bureau of Census in the year 1850 the population of the US was 23,191,876 in 1900 the population was 62,947,714

A. Assuming that the population grew exponentially during the period compute
the growth constant k.

B. Assuming continued growth at the same rate predict the 1950 population

• Math -

p =pi e^kt
let t = 0 at 1850
so pi = 23,191,876
p = 23,191,876 e^kt
in 1900 t = 1900-1850 = 50
so
62,947,714 = 23,191,876 e^50k
1.275 = e^50k
take ln of both sides
50 k = .2429
k = .00486

P at t is 100 years = 23,191,876 e^(.486)
= 23,191,876 (1.6258)
=37,705,351
I approximated all the natural logs so you should do the arithmetic more accurately although obviously the census and law are not that accurate anyway.

• Math correction -

p =pi e^kt
let t = 0 at 1850
so pi = 23,191,876
p = 23,191,876 e^kt
in 1900 t = 1900-1850 = 50
so
62,947,714 = 23,191,876 e^50k
2.714 = e^50k
take ln of both sides
50 k = .9984
k = .01997

P at t is 100 years = 23,191,876 e^(1.997)
= 23,191,876 (7.367)
=170,852,745
I approximated all the natural logs so you should do the arithmetic more accurately although obviously the census and law are not that accurate anyway.

• Math -

THank you so much

## Similar Questions

1. ### math

According to data from the U.S. Census Bureau, the population P of Cleveland, Ohio (in thousands) in year x can be approximated by the equation P = .08x^2 - 13.08x + 927 , where x = 0 corresponds to the year 1950. In what year (in …
2. ### Algebra 2

According to the US Census Bureau, the population of the United States has been growing at an average rate of approximately 2% per year. The census is taken every 10 years, and the population in 1980 was estimated at 226 million people. …
3. ### Alegebra I

I need help please!!! On January 1, 2010, Chessville has a population of 50,000 people. Chessville then enters a period of population growth. Its population increases 7% each year. On the same day, Checkersville had a population of …
4. ### Algebra

On Jan 1, 2010, Chessville has a population of 50,000 people. Chessville then enters a period of population growth. Its population increases 7% each year. On the same day, Checkersville has a population of 70,000 people. Checkersville …
5. ### Algebra

On Jan 1, 2010, Chessville has a population of 50,000 people. Chessville then enters a period of population growth. Its population increases 7% each year. On the same day, Checkersville has a population of 70,000 people. Checkersville …
6. ### Algebra

On Jan 1, 2010, Chessville has a population of 50,000 people. Chessville then enters a period of population growth. Its population increases 7% each year. On the same day, Checkersville has a population of 70,000 people. Checkersville …
7. ### Algebra

On Jan 1, 2010, Chessville has a population of 50,000 people. Chessville then enters a period of population growth. Its population increases 7% each year. On the same day, Checkersville has a population of 70,000 people. Checkersville …
8. ### Precalculus

The population of the US in 1850 was 23191876. In 1900, the population was 62947714. a. assuming that the population grew exponentially, compute the grownth constant. b. assuming continued growth at a constant rate, predict the population …
9. ### Science help urgent :/

What has been the general trend in human population growth?
10. ### Algebra

On January 1, 2010, Chessville has a population of 50,000 people. Chessville then enters a period of population growth. Its population increases 7% each year. On the same day, Checkersville has a population of 70,000 people. Checkersville …

More Similar Questions