Calculus
posted by Z32 .
The population of a region is growing exponentially. There were 40 million people in 1980 (when t=0) and 50 million people in 1990. Find an exponential model for the population (in millions of people) at any time t, in years after 1980.
P(t)=
Predicted population in the year 2000 = _______million people.
What is the doubling time?
Doubling time = _______ years.

Since one of the questions deals with "doubling time", I will use 2 as the base.
(Of course we could use any base, many mathematicians would automatically use e as the base.)
P(t) = a(2)^(kt) , where P(t) is the population in millions, a is the beginning population, and t is the time in years.
clearly , a = 40
P(t) = 40(2)^(kt)
when t=10, (1990), N = 50
50 = 40(2)^(10k)
1.25 = 2^(10k)
take the ln of both sides, hope you remember your log rules
10k = ln 1.25/ln 2
10k = .32193
k = .032193
so P(t) = 40(2)^(.032193t)
in 2000, t = 20
P(20) = 40(2)^(.032193(20))
= 62.5 million
for the formula
P(t) = a(2)^(t/d), d = the doubling time
so changing .032193t to t/d
= .032193t
= t/31.06
so the doubling time is 31.06
another way would be to set
80 = 40(2)^(.032193t)
2 = (2)^(.032193t)
.032193t = ln 2/ln 2 = 1
t = 31.06 
Curiously, this is very close to the current population doubling time for India.
Respond to this Question
Similar Questions

MATH
A table of the U.S. population in millions indicated in 1960 the population was 181 million, in 1970 the population was 205 million, in 1980 the population was 228 million, and in 1990, the population was 250 million. Describe the … 
Math AP Calc
In 1951, the population of India was 357 million people. By 1981 it had grown to 984 million. If the population is growing exponentially, when (in what month of what year) will the population reach 1 billion people? 
Math
I have no idea how to even start this problem. In 1951, the population of India was 357 million people. By 1981 it had grown to 984 million. If the population is growing exponentially, when (in what month of what year) will the population … 
Math
In 1951, the population of India was 357 million people. By 1981 it had grown to 984 million. If the population is growing exponentially, when (in what month of what year) will the population reach 1 billion people? 
MathReiny Help! Previous Problem
In 1951, the population of India was 357 million people. By 1981 it had grown to 984 million. If the population is growing exponentially, when (in what month of what year) will the population reach 1 billion people? 
Calculus
Year 1960 1970 1980 1990 2000 Rate 39 59 64 89 106 of change (million people per year) Use this data to sketch a graph like that in Figure 5.2 on page 238. Draw rectangles on this graph (as in Figure 5.2) to help you underestimate … 
calculus
The population of a country was 8.4 million people in 2000. Three years later, the population of the same nation was 9.3 million people. Assuming that population is growing exponentially, what is the projected population (rounded to … 
6th grade Math
I need some help figuring out how to work the word problem below. It says in 2000, the population of the United States was 280 million people. Between 1990 and 2000, the population grew by about 12%. What was the US population in 1990? 
algebra
In 1990, the population of Africa was 643 million and by 2000 it had grown to 813 million. a.) Use the exponential growth model A=A0 e^kt, in which t is the number of years after 1990, to find the exponential growth function that models … 
Calc
Year 1940 1950 1960 1970 1980 Rate of change (million people per year) 29 49 67 76 98 If the population in 1940 were 2158 million and if the population in 1980 were 4846 million, what would be the true total change in population?