GATE Exam > GATE Questions > The population of a new city is 5 million and...
Start Learning for Free
The population of a new city is 5 million and is growing at 20% annually. How many years would it take to double at this growth rate?
- a)3-4 years
- b)4-5 years
- c)5-6 years
- d)6-7 years
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The population of a new city is 5 million and is growing at 20% annual...
Most Upvoted Answer
The population of a new city is 5 million and is growing at 20% annual...
Given:
Population of a new city = 5 million
Annual growth rate = 20%
To find:
The number of years it would take for the population to double at this growth rate.
Solution:
Let's assume the initial population of the city is P.
After 1 year, the population will be P + 20% of P = P(1 + 0.2) = 1.2P
After 2 years, the population will be 1.2P + 20% of 1.2P = 1.2P(1 + 0.2) = 1.44P
After 3 years, the population will be 1.44P + 20% of 1.44P = 1.44P(1 + 0.2) = 1.728P
We observe that after each year, the population is multiplied by a factor of (1 + 0.2) = 1.2.
To find the number of years it would take for the population to double, we need to solve the equation:
1.2^x * P = 2P
Dividing both sides by P, we get:
1.2^x = 2
Taking the logarithm of both sides, we get:
x * log(1.2) = log(2)
Simplifying further, we get:
x = log(2) / log(1.2)
Using a calculator, we find that x ≈ 3.8.
Therefore, it would take approximately 3-4 years for the population of the city to double at a growth rate of 20%.
Answer:
Option A) 3-4 years
Population of a new city = 5 million
Annual growth rate = 20%
To find:
The number of years it would take for the population to double at this growth rate.
Solution:
Let's assume the initial population of the city is P.
After 1 year, the population will be P + 20% of P = P(1 + 0.2) = 1.2P
After 2 years, the population will be 1.2P + 20% of 1.2P = 1.2P(1 + 0.2) = 1.44P
After 3 years, the population will be 1.44P + 20% of 1.44P = 1.44P(1 + 0.2) = 1.728P
We observe that after each year, the population is multiplied by a factor of (1 + 0.2) = 1.2.
To find the number of years it would take for the population to double, we need to solve the equation:
1.2^x * P = 2P
Dividing both sides by P, we get:
1.2^x = 2
Taking the logarithm of both sides, we get:
x * log(1.2) = log(2)
Simplifying further, we get:
x = log(2) / log(1.2)
Using a calculator, we find that x ≈ 3.8.
Therefore, it would take approximately 3-4 years for the population of the city to double at a growth rate of 20%.
Answer:
Option A) 3-4 years
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
The population of a new city is 5 million and is growing at 20% annually. How many yearswould it take to double at this growth rate?a)3-4 yearsb)4-5 yearsc)5-6 yearsd)6-7 yearsCorrect answer is option 'A'. Can you explain this answer?
Question Description
The population of a new city is 5 million and is growing at 20% annually. How many yearswould it take to double at this growth rate?a)3-4 yearsb)4-5 yearsc)5-6 yearsd)6-7 yearsCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The population of a new city is 5 million and is growing at 20% annually. How many yearswould it take to double at this growth rate?a)3-4 yearsb)4-5 yearsc)5-6 yearsd)6-7 yearsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The population of a new city is 5 million and is growing at 20% annually. How many yearswould it take to double at this growth rate?a)3-4 yearsb)4-5 yearsc)5-6 yearsd)6-7 yearsCorrect answer is option 'A'. Can you explain this answer?.
The population of a new city is 5 million and is growing at 20% annually. How many yearswould it take to double at this growth rate?a)3-4 yearsb)4-5 yearsc)5-6 yearsd)6-7 yearsCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The population of a new city is 5 million and is growing at 20% annually. How many yearswould it take to double at this growth rate?a)3-4 yearsb)4-5 yearsc)5-6 yearsd)6-7 yearsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The population of a new city is 5 million and is growing at 20% annually. How many yearswould it take to double at this growth rate?a)3-4 yearsb)4-5 yearsc)5-6 yearsd)6-7 yearsCorrect answer is option 'A'. Can you explain this answer?.
Solutions for The population of a new city is 5 million and is growing at 20% annually. How many yearswould it take to double at this growth rate?a)3-4 yearsb)4-5 yearsc)5-6 yearsd)6-7 yearsCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of The population of a new city is 5 million and is growing at 20% annually. How many yearswould it take to double at this growth rate?a)3-4 yearsb)4-5 yearsc)5-6 yearsd)6-7 yearsCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The population of a new city is 5 million and is growing at 20% annually. How many yearswould it take to double at this growth rate?a)3-4 yearsb)4-5 yearsc)5-6 yearsd)6-7 yearsCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for The population of a new city is 5 million and is growing at 20% annually. How many yearswould it take to double at this growth rate?a)3-4 yearsb)4-5 yearsc)5-6 yearsd)6-7 yearsCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of The population of a new city is 5 million and is growing at 20% annually. How many yearswould it take to double at this growth rate?a)3-4 yearsb)4-5 yearsc)5-6 yearsd)6-7 yearsCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The population of a new city is 5 million and is growing at 20% annually. How many yearswould it take to double at this growth rate?a)3-4 yearsb)4-5 yearsc)5-6 yearsd)6-7 yearsCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup