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April 1, 2015

Posted by **Nikki** on Monday, January 18, 2010 at 9:16pm.

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 -
**Damon**, Monday, January 18, 2010 at 10:08pmp =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 -
**Damon**, Monday, January 18, 2010 at 10:17pmp =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 -
**Nikki**, Monday, January 18, 2010 at 10:51pmTHank you so much

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