If a population consists of ten thousand individuals at time t=0 (P0), and the annual growth rate (excess of births over deaths) is 3% (GR), what will the population be after 1, 15, and a 100 years (n)? Calculate the "doubling time" for this growth rate. Given this growth rate, how long would it take for this population of a hundred thousand individuals to reach 1.92 million? one equation that may be useful is:

Question

If a population consists of ten thousand individuals at time t=0 (P0), and the annual growth rate (excess of births over deaths) is 3% (GR), what will the population be after 1, 15, and a 100 years (n)? Calculate the "doubling time" for this growth rate. Given this growth rate, how long would it take for this population of a hundred thousand individuals to reach 1.92 million? one equation that may be useful is:

Pt=Po * (1+ {GR/100})n

Additionally, using the current world population from the census website, calculate world population in 2100 with growth rates of 2.3% and 0.5% why is this important?

Answer 1

The first part of the question has been answered before. See:

http://www.jiskha.com/display.cgi?id=1254881441

For the second part of the question, it is essentially the same idea. By using the formula
P(2100)=P(2009)*(1+r)^(2100-2009)
where
P(t) = projected population in year t
r = rate of growth, for example, 0.023 or 0.005

If you need more help, post any time.

Answer 2

Your equation should be

Pt=Po * (1+ {GR/100})^n
The n is an exponent.

Why don't you just apply the formula?

After 100 years,
Pt/Po = (1.03)^100 = 19.2

Note that ratio also equals
1.92 million/100,000

The population doubling time is about 24 years. There is a handy approximate rule of thumb that says
(growth rate, %)*(doubling time, years) = 72

The exact answer is
log2/(log 1.03) = 23.45 years

Answer 3

To calculate the population after a certain number of years, you can use the formula provided:

Pt = Po * (1 + (GR/100))^n

Let's calculate the population after 1 year, 15 years, and 100 years using the given information:

1. After 1 year (n = 1):
P1 = P0 * (1 + (GR/100))^1
= 10,000 * (1 + 3/100)
= 10,000 * 1.03
= 10,300

So, the population after 1 year would be 10,300.

2. After 15 years (n = 15):
P15 = P0 * (1 + (GR/100))^15
= 10,000 * (1 + 3/100)^15
≈ 10,000 * (1.03)^15
≈ 10,000 * 1.520094
≈ 15,200.94

So, the population after 15 years would be approximately 15,200.94.

3. After 100 years (n = 100):
P100 = P0 * (1 + (GR/100))^100
= 10,000 * (1 + 3/100)^100
≈ 10,000 * (1.03)^100
≈ 10,000 * 2.704813
≈ 27,048.13

So, the population after 100 years would be approximately 27,048.13.

Now let's calculate the doubling time, which is the time it takes for the population to double in size at the given growth rate.

Doubling time (t2) can be calculated using the formula:
t2 = ln(2) / (GR/100)

Here, ln denotes the natural logarithm.

t2 = ln(2) / (3/100)
≈ 0.693 / 0.03
≈ 23.1 years

So, the doubling time for this growth rate is approximately 23.1 years.

To calculate how long it would take for a population of 100,000 to reach 1.92 million, we can rearrange the formula as follows:

n = log(1.92) / log(1 + (GR/100))

Here, log denotes the logarithm.

n = log(1.92) / log(1 + (3/100))
≈ 0.283 / 0.03
≈ 9.43 years

So, it would take approximately 9.43 years for the population to reach 1.92 million.

Now, regarding the world population in 2100 with different growth rates - 2.3% and 0.5% - it is important because it helps us understand and plan for the future. Population growth impacts various aspects of society, such as resource availability, infrastructure needs, environmental impact, and more. By analyzing different growth rate scenarios, we can make informed decisions to address potential challenges and create sustainable solutions.