Question

- The population of a town is 6,00,000. If birth rate is 7.5% p.a. and the death rate is 4.5% p.a.
Find the population of town after 1 ×1/2


please answer​

Answer 1

Answer: ≈ 6,276,00

Given that:

• Birth rate, b = 7.5/100 = 0.075 p.a
• Death rate, d = 4.5/100 = 0.045 p.a
• Current population, p = 6,00,000

We converted birth and death rate percentage into rate by dividing it by 100.

To Find:

• Population after 1 × 1/2 years or 1 year 6 months.

Solution:

We can solve it by applying the concept of Compound Interest. So, we have

• Principal value, p = 6,00,000
• Interest rate, r = b - d = 0.075 - 0.045 = 0.03
• Time, t = 18 months or 1.5 years
• n = 12 times per year or Compounded monthly

Now,

=> p" = p(1 + r/n)^(nt)

=> p" = 6,00,000 ( 1 + 0.03/12 )^(12×1.5)

=> p" = 6,00,000 (1.0025)^(18)

=> p" ≈ 6,00,000 × 1.046

=> p" ≈ 6,27,600

Hence, The population after one and a half year will be approx. 6,27,600.

Answer 2

✴ Given :-

• ➬ Population of town = 600000
• ➬ Birth rate = 7.5 %
• ➬ Death rate = 4.5 %

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

✴ To Find :-

• ➬ Population after 1 × 1/2 years .

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

✴ Solution :-

❒ Formula Applied :

$\large{\blue{\bigstar}}{\underline{\boxed{\red{\sf{P_{1.5\: years} = P\bigg(1 + \dfrac{R}{N} \bigg)^ {n \times t}}}}}}$

Here :

• ➳ P_1.5 = ?
• ➳ Interest rate = R = 0.03 %
• ➳ Time = 18 months or 1.5 years
• ➳ n = 12 months
• ➳ Compounded = Monthly

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Finding the Population :

$\qquad{\dashrightarrow{\qquad{\sf{P_1.5 = P\bigg(1 + \dfrac{R}{N} \bigg)^ {n \times t}}}}}$

$\qquad{\dashrightarrow{\qquad{\sf{P_{1.5} = 600000\bigg(1 + \dfrac{0.03}{12} \bigg)^ {12 \times 1.5}}}}}$

$\qquad{\dashrightarrow{\qquad{\sf{P_{1.5} = 600000\bigg(1 + {1.0025} \bigg)^ {18}}}}}$

$\qquad{\dashrightarrow{\qquad{\sf{P_{1.5} = 600000 ×1.046 }}}}$

$\qquad{\qquad{\large{\red{:\longmapsto{\underline{\overline{\boxed{\green{\sf{ 627600}}}}}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Therefore :

❝ Population after 1 × 1/2 years is 627600 .❞

${\pink{\underline{▬▬▬▬▬}}}{\color{darkblue}{\underline{▬▬▬▬▬}}}{\orange{\underline{▬▬▬▬▬}}}{\red{\underline{▬▬▬▬▬▬}}}$