Certainly! Let's work through the problem step-by-step to determine the population of the town in the year 2016 and the year 2020, given that the population in 2018 was 238,765 and the annual growth rate is 6%.
### Step-by-Step Solution:
#### 1. Understanding the Growth Rate:
- The growth rate is 6% per annum, which can be expressed as a decimal for calculation purposes: 0.06.
#### 2. Finding the Population in the Year 2016:
- To find the population for a past year, we need to consider the reverse growth rates. This means we will divide the population of 2018 by the growth factor raised to the power of the number of years back.
- The number of years back from 2018 to 2016 is: [tex]\(2\)[/tex] years.
- The growth factor for a 6% growth rate can be calculated as: [tex]\(1 + 0.06 = 1.06\)[/tex].
- Therefore, for 2 years backward, the population in 2016 can be found by dividing the population in 2018 by [tex]\(1.06^2\)[/tex].
#### 3. Finding the Population in the Year 2020:
- To find the population for a future year, we need to multiply the current population by the growth factor raised to the power of the number of years forward.
- The number of years forward from 2018 to 2020 is: [tex]\(2\)[/tex] years.
- The growth factor for a 6% growth rate can be calculated as: [tex]\(1 + 0.06 = 1.06\)[/tex].
- Therefore, for 2 years forward, the population in 2020 can be found by multiplying the population in 2018 by [tex]\(1.06^2\)[/tex].
### Calculations:
#### Population in 2016:
[tex]\[ \text{Population in 2016} = \frac{238,765}{(1.06)^2} \][/tex]
After performing the calculation, we find:
[tex]\[ \text{Population in 2016} \approx 212,500 \][/tex]
#### Population in 2020:
[tex]\[ \text{Population in 2020} = 238,765 \times (1.06^2) \][/tex]
After performing the calculation, we find:
[tex]\[ \text{Population in 2020} \approx 268,276 \][/tex]
### Final Answer:
- The population of the town in the year 2016 was approximately 212,500.
- The population of the town in the year 2020 was approximately 268,276.
