Answer:
208 million
Step-by-step explanation:
In this situation, the population in 1991, 200 million is the initial value. The end year, 2011 is 20 years after the initial year because 2011 - 1991 = 20.
The formula for exponential growth is [tex]y = ab^{x}[/tex]
y is the ending value, ending population in this case.
a is the initial value, 200 million in population.
b is the growth rate.
x is the time passed, 20 years.
Use the exponential formula to calculate growth rate.
Use the other given information:
1991 it was 200 million
2000 it was 204 million
The population can be found in hundreds for millions so that it's simpler.
In the formula, use the later population as the end value (y = 204). The time elapsed, x, is 2000-1991. (x = 9). The initial population is 200 million (a = 200).
Substitute these values then find b, the variable for growth rate.
[tex]y = ab^{x}[/tex]
[tex]204 = (200)b^{9}[/tex]
[tex]204/200 = b^{9}[/tex]
[tex]1.02 = b^{9}[/tex]
You can use guess and check for an approximate answer.
Substitute a guess for b. Find a number that when raised to the power of 9, it is close to 1.02.
Guess for b Check Too high or low
1.1 2.36 high
1.001 1.01 low
1.002 1.018 close enough
b = 1.002
Use the information to solve, where:
y = ?, the population for the year 2011
a = 200, (actually 200 million)
b = 1.002
x = 20 (the difference between 1991 and 2011)
Substitute into the formula:
[tex]y = ab^{x}[/tex]
[tex]y = 200(1.002)^{20}[/tex]
[tex]y = 208.154[/tex]
y ≈ 208 <= Rounded
*Remember the population is not 208, but 208 million
Therefore the population in 2011 is about 208 million.
