Is it linear or exponential growth

[Guest]

The question is :
In 2018, the population in China was 1,427,647,786.
According to data, China’s population growth rate is 0.59% per year. What will the population be in China in 2021?
A) 8,423,121
B) 1,436,070,908
C) 1,444,543,726
D) 1,452,917,152
E) 1,453,142,111
The book answer is (E). But I think it is linear growth because it is only 3 years.
My solution is : The population in 2021 = 1427647786 + 142647786(.0059)3=1452917152 . which is in choice (D) not (E).
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Please , I need help. What is the mistake in my solution.
Thank you very much.

[Guest]

"But I think it is linear growth because it is only three years."
I have no idea why you think whether growth is linear or exponential depends on how long a time you are dealing with!

"China's population growth rate is 0.59%"
Since the growth rate is a constant, the growth must be exponential!

The population in 2018 was 1,427,647,786.

Since the population increased by 0.57% the next year, 2019, the population is
(1.0057)(1,427,647,786)= 1,435,785,378

The next year, 2020, the population is
(1.0057)(1435785378)= 1,443,969,355

The next year, 2021, the population is
(1.0057)(1,443,969,355)= 1,452,199,980

That's closer to D than to E but it certainly is NOT linear!

[Guest]

Since I cannot edit on this board I have to repeat that post but with the correct 0.59% rather than 0.57%.

"But I think it is linear growth because it is only three years."
I have no idea why you think whether growth is linear or exponential depends on how long a time you are dealing with!

"China's population growth rate is 0.59%"
Since the growth rate is a constant, the growth must be exponential!

The population in 2018 was 1,427,647,786.

Since the population increased by 0.59% the next year, 2019, the population is
(1.0059)(1,427,647,786)= 1,436,070,908

The next year, 2020, the population is
(1.0059)(1,436,070,908)= 1,444,543,726

The next year, 2021, the population is
(1.0059)(1,444,543,726)= 1,453,066,534

That is, of course, the same as [tex](1,427,647,786)(1.0057)^3[/tex].

That's not exactly E but it is close. And it is defintely NOT linear.

"Linear growth" is when the increase is the same amount each year.

"Exponential growth" is when the increase is the same percent each year.

[mahmoud1945]

Thank you very much for your reply.
I think linear not exponential because people not growth very rapidly as bacteria.
The bacteria has exponential growth in few moments because the new generation make another newer generation.
But people in 3 years, the new children cannot make another new children in 3 years. For this reason I think, in 3 years the linear growth is the more correct.
Thank you very much. I still need your help and your idea.

[Guest]

All you are saying is that you do NOT KNOW what "linear growth" is. As I said in my first response linear growth requires the same increase in each time unit.

[Guest]

To calculate the population in China in 2021 using a growth rate, we need to use the formula for exponential growth rather than linear growth. Exponential growth takes into account the compounding effect of the population growth rate over multiple years. The formula for exponential growth is:
P(t)=P0×(1+r)^t
where:
P(t) is the population at time t,
P0 is the initial population,
r is the growth rate,
t is the number of years.
Given:
Initial population P0=11,427,647,786
Annual growth rate r=0.59%=0.0059,
Time t=3 years (from 2018 to 2021).
We can now calculate the population in 2021:
P(3)=1,427,647,786×(1+0.0059)^3
First, calculate the growth factor for 3 years:
(1+0.0059)^3=1.0059^3
Using a calculator:
1.0059^3≈1.01776
Now, multiply this factor by the initial population:
P(3)≈1,427,647,786×1.01776
P(3)≈1,452,917,152
Therefore, the population of China in 2021 is approximately 1,452,917,152, which corresponds to option (D).
So the correct answer should indeed be (D), not (E). Your understanding is correct, and the mistake in the book answer appears to be due to an incorrect calculation. The population in 2021, considering exponential growth over 3 years at a 0.59% annual growth rate, should be approximately 1,452,917,152.


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[mycalsuite]

The question is :
In 2018, the population in China was 1,427,647,786.
According to data, China’s population growth rate is 0.59% per year. What will the population be in China in 2021?
A) 8,423,121
B) 1,436,070,908
C) 1,444,543,726
D) 1,452,917,152
E) 1,453,142,111
The book answer is (E). But I think it is linear growth because it is only 3 years.
My solution is : The population in 2021 = 1427647786 + 142647786(.0059)3=1452917152 . which is in choice (D) not (E).
-------------
Please , I need help. What is the mistake in my solution.
Thank you very much.

P= 1,427,647,786 *(1.0059)^3 = 1,453,142,111 --- answer (E)