Question

In 1992, the countries Chad and Denmark each had population of about 5.2 million. However,

the exponential growth rate for Chad was 2.5% per year, which Denmark was 0.1% per year. Find the
population of Denmark when the population of Chad was 10 million people. (Round time to the nearest
tenth, and population to the nearest person).

Answer 1

9514 1404 393

Answer:

5,339,479

Explanation:

The populations in millions of the different countries can be represented by the equations ...

c = 5.2(1.025^t)

d = 5.2(1.001^t)

We want to find d when c = 10. Solving for t when c=10, we have ...

10 = 5.2(1.025^t)

10/5.2 = 1.025^t

log(10/5.2) = t×log(1.025)

t = log(10/5.2)/log(1.025)

Then the value of d for that value of t is ...

d = 5.2(1.001^(log(10/5.2)/log(1.025)) ≈ 5.3394789

The population of Denmark is about 5,339,479 when the population of Chad is 10 million.

_____

If we round the number of years to 26.5 before computing the population of Denmark, we get 5,339,571 -- about 92 more people. Ordinarily, one would not round intermediate results.