Posted by **Andy G** on Monday, March 17, 2014 at 8:53pm.

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 in 1950.

- Precalculus -
**Reiny**, Monday, March 17, 2014 at 9:38pm
let t=0 correspond with the year 1850

then 1900 ---> t = 50

then 1950 ---> t = 100

population = a( e^(kt) ) , where a is the initial population and t is the number of years since 1850

23,191,876 = a e^0

a = 23,191,876

then:

62,947,714 = 23,181,876 e^(50k)

2.715384812 = e^(50k)

50k = ln(2.715384812 )

k = .019978673

in 1950

pop = 23,191,876 e^(100( .019978673))

= 170,927,267

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