Question

Sweden’s population was 5.14 million in 1900 and 8.86 million in 2000. How many people lived in Sweden when King Karl XII died in 1718 if the population increase has been exponential since then?

Answer 1

Explanation:

To solve this problem, we need to use exponential growth formula, which is:

P = P0 * e^(rt)

where P is the final population, P0 is the initial population, r is the annual growth rate, and t is the time in years.

We can use the given data to find the annual growth rate r:

r = ln(P/P0) / t

where ln is the natural logarithm.

Using the population data from 1900 and 2000, we get:

r = ln(8.86/5.14) / 100 ≈ 0.0198

So the annual growth rate is approximately 0.0198, or 1.98%.

Now, we need to find the initial population P0 when King Karl XII died in 1718. Let's call this population X.

We know that the population has been growing exponentially since then, so we can use the formula above to relate the population in 1718 to the population in 1900:

X * e^(0.0198 * 182) = 5.14 million

where 182 is the number of years between 1718 and 1900.

Solving for X, we get:

X = 5.14 million / e^(0.0198 * 182) ≈ 0.14 million

Therefore, the population of Sweden when King Karl XII died in 1718 was approximately 0.14 million people.