2. A country has a doubling time for its people of 20 years. If it ends up with 80 million people after 60 years, how many people did it have to start with (in this questions)?

in 60 years, it has doubled three times, giving 8 times the original population.

So, what is 1/8 of 80?

10

Well, if the country has a doubling time of 20 years, I'd say they must have started with zero people, because otherwise, the country would have had to go back in time to have a negative population. So, let's assume they started from scratch and built up to 80 million people in 60 years. That's quite an achievement, don't you think? Punchline: From zero to 80 million in just 60 years! That's called population progress!

To find out how many people the country had to start with, we can use the concept of exponential growth and the formula for doubling time.

Doubling time is the amount of time it takes for a population to double in size. In this case, the doubling time is given as 20 years.

Using this information, we can find the growth rate (r) using the formula:

r = 70 / doubling time

r = 70 / 20

r = 3.5%

Now, we can use the formula for exponential growth to calculate the initial population size (P0). The formula is:

P = P0 * (1 + r/100)^n

Where:
P0 = initial population size
P = final population size
r = growth rate
n = number of time periods (years in this case)

We know that after 60 years, the population became 80 million people (P = 80 million).

Plugging in the values, we have:

80 million = P0 * (1 + 3.5/100)^60

Dividing both sides by (1 + 3.5/100)^60, we get:

P0 = 80 million / (1 + 3.5/100)^60

Calculating this expression, we find:

P0 ≈ 80 million / 1.035^60 ≈ 80 million / 2.208 ≈ 36.2 million

Therefore, the country had approximately 36.2 million people to start with.

To find the initial population of the country, we can use the concept of population doubling time.

The doubling time refers to the time it takes for a population to double in size. In this case, we are given that the doubling time for the country is 20 years.

To determine the initial population, we can use the following formula:

Initial Population = Final Population / (2^(Time / Doubling Time))

Given that the final population is 80 million (80,000,000) and the time is 60 years, we can substitute these values into the formula:

Initial Population = 80,000,000 / (2^(60 / 20))

Simplifying further:

Initial Population = 80,000,000 / (2^3)

To compute 2^3, we raise 2 to the power of 3, which yields 8:

Initial Population = 80,000,000 / 8

Final calculation:

Initial Population = 10,000,000

Therefore, the country had 10 million people to start with for the given scenario.