Question

The population of a city increases each year by 4% of what it had been at the beginning of each year. If its present population is 6760000, find: its population 2 years hence is approx. 7058522.
a. True
b. False

Answer 1

Hint—We need to find the population after 2 years and for that we need to calculate the population in the first year and then for the second year. So, to calculate the population in the first year, find the 4% of the current population and add it with the current population. Here, the current population is given in the question, then calculate the population for the second year by finding the 4% of the current population and add it into the current population obtained. Here, the current population is the population obtained after 1 year

Complete step-by-step solution
Consider the given data,
We have been given the current population which is equal to 676000 and the rate at which the population of a city increases each year is 4% of what it had been at the beginning of each year.
Now, we will find the population after 2 years.
So, starting with the population after 1st year,
We get,
\[
  {\text{Population}} = 676000 + \dfrac{4}{{100}} \times 676000 \\
   = 7030400 \\
\]
Hence, the population is approx. 7030400 after 1 year.
Now, we will find the population after 2nd year,
Here, we will consider the current population as 703400 that is what we have got at the end of 1st year and the rate will remain the same that is 4%.
So,
\[
  {\text{Population}} = 7030400 + \dfrac{4}{{100}} \times 7030400 \\
   = 7311616 \\
 \]
Hence, the population is approx. 7311616 after 2 years.
Since, we are given in the question that the population of the city after 2 years is 7058522 but we have found in the solution that the population of the city after 2 years is 7311616.
Hence, the statement is false.
Note: When finding the population for the 2nd year, the current population will be the population obtained at the end of first year. The percentage of rate will remain the same for both the years. Do not use the given population for finding all the populations of the further years. The rate should be multiplied with the current population and then add it to estimate the population for that year.