Precalculus
posted by Andy G .
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
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
Respond to this Question
Similar Questions

Algerba
Pick a country of your choice that is experiencing population growth. find the most recent population count of the country you have chosen and the population growth rate of that country. Use that growth rate to approximate the population … 
Math
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. … 
maths
The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 2015. 
Trigonometry
In 2010, the population of a country was 70 million and growing at a rate of 1.9% per year. assuming the percentage growth rate remains constant express the population P, as a function of t, the number of years after 2010. 
science
Linear growth a. is characterized by a rapidly growing population. b. is demonstrated by the sequence 12, 13, 14, 15, 16. c. is illustrated by the numbers 2, 4, 8, 16, 32. d. is characterized by resource use and consumption. e. is … 
Algebra 2
Recursion formula for a given population for each interval,n, at a time, and k is a constant called the Malthusian factor: a_n=ka_n1(1a_n1)  Assuming n is measured in weeks, calculate the insect population for weeks 2, 3, and 4 … 
Science help urgent :/
What has been the general trend in human population growth? 
maths
The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 1991. 
Calculus
assuming the population of the earth changes at a rate proportional to the current population further, it is estimated that at time t=0, the earth's population was 600 million, at t=300, it's population was 2.8 billion. find an expression … 
Calculus
Assuming the population of the earth changes at a rate proportional to the current population further, it is estimated that at time t=0, the earth's population was 600 million, at t=300, it's population was 2.8 billion. find an expression …