If each year the population of the country grows by 20%, how many years will elapse before the population of the country doubles?
A. 3
B. 4
C. 5
D. 6
E. 7
OA: B
A. 3
B. 4
C. 5
D. 6
E. 7
OA: B
If the population of the country grows by 20% each year, the population the next year will be 120% of the year before, or
$$1.2\cdot previous\ population$$
For each year, we'll multiply by 1.2 again. So after one year, the population will be
$$1.2\cdot original\ population$$
After two years, the population will be
$$1.2\cdot1.2\cdot original\ population=1.44\cdot original\ population$$
After three years, the population will be
$$1.44\cdot1.2\cdot original\ population=1.728\cdot original\ population$$
After four years, the population will be
$$1.728\cdot1.2\cdot original\ population=2.0736\cdot original\ population$$
We want to find how many years it will take to double the population, or
$$2\cdot original\ population$$
The population has slightly more than doubled after 4 years, so the answer is B.
Note: we could also express the equation for the country's population as $$1.2^x\cdot original\ population$$ where x is the number of years that have elapsed. Then we can set this equal to our expression for doubling the population: $$1.2^x\cdot original\ population=2\cdot original\ population$$ $$1.2^x=2$$ and then solve for x.
