Question 1173638: A national census is mandated by the Constitution of Pakistan to be held every ten years. After
the independence of Pakistan in 1947, the first census took place in 1951. Figure 1 reflects the
increase in population of Pakistan during last four national census. The increase between 1972 and
2017 could be approximated by a linear function. If in 1972 the population was 65.309 million
and as per the census data of 2017 the population was 207.774 million;
a) Determine the estimation function P = f (t), where P equals the population of Pakistan and t
equals time measured in years since 1972.
b) Interpret the slope and P intercept
c) According to this function, what will be the estimated population of Pakistan in 2027 census?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down this population estimation problem.
**a) Determine the Estimation Function P = f(t)**
1. **Define the Points:**
* (t1, P1) = (0, 65.309 million) - 1972 is the starting year, so t=0.
* (t2, P2) = (45, 207.774 million) - 2017 is 45 years after 1972.
2. **Calculate the Slope (m):**
* m = (P2 - P1) / (t2 - t1)
* m = (207.774 - 65.309) / (45 - 0)
* m = 142.465 / 45
* m ≈ 3.165888888888889 (approximately 3.166 million per year)
3. **Determine the P-intercept (b):**
* Since we're using 1972 as t=0, the P-intercept is the population in 1972, which is 65.309 million.
4. **Write the Linear Equation (P = mt + b):**
* P = 3.166t + 65.309
Therefore, the estimation function is P = 3.166t + 65.309.
**b) Interpret the Slope and P-intercept**
* **Slope (3.166):** The slope represents the average annual increase in Pakistan's population (in millions) between 1972 and 2017. In this case, the population increased by approximately 3.166 million people per year.
* **P-intercept (65.309):** The P-intercept represents the estimated population of Pakistan in 1972, which was 65.309 million.
**c) Estimated Population in 2027 Census**
1. **Calculate the Time (t):**
* 2027 - 1972 = 55 years
2. **Plug t into the Equation:**
* P = 3.166 * 55 + 65.309
* P = 174.13 + 65.309
* P = 239.439 million
Therefore, according to this linear function, the estimated population of Pakistan in 2027 would be approximately 239.439 million.
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