John158
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Can someone tell me how to do this?

The global human population was approximately 1.6x10^9 in 1900, and 6.1x10^9 in 2000. The population dynamics can be modelled by the exponential growth formula Nt = N0e kt.

Rate = 6.1 x 10^10 – 1.6 x 10^10 / 1.6 x 10^10
= 2.812500 x 10^0
2.812500 x 10^0/ 100 = 281.25 %


d) Assuming that this rate of exponential growth also applied before 1900, estimate what the global population was in the year 1800, to an appropriate number of significant figures
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Ira :)
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Could you upload a pic of the entire question (including a, b, c)?
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old_engineer
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(Original post by John158)
Can someone tell me how to do this?

The global human population was approximately 1.6x10^9 in 1900, and 6.1x10^9 in 2000. The population dynamics can be modelled by the exponential growth formula Nt = N0e kt.

Rate = 6.1 x 10^10 – 1.6 x 10^10 / 1.6 x 10^10
= 2.812500 x 10^0
2.812500 x 10^0/ 100 = 281.25 %


d) Assuming that this rate of exponential growth also applied before 1900, estimate what the global population was in the year 1800, to an appropriate number of significant figures
The information given to you in the question is:

N_{1900}=1.6 \times 10^{9}=N_0e^{1900k}
N_{2000}=6.1 \times 10^{9}=N_0e^{2000k}

To find the value of k, you can divide one of those equations by the other (which eliminates N_0). Then to find the value of N_0 you can substitute your value for k into one of the equations above.
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John158
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Sorry I am still having problems understanding.

This is the full thing:

The global human population was approximately 1.6x10^9 in 1900, and 6.1x10^9 in 2000. The population dynamics can be modelled by the exponential growth formula Nt = N0e kt.

a) Using the above information, write a general expression for the rate constant k and then evaluate this expression to evaluate this constant to 3 significant figures (Use years as the unit of time).


b) Calculate the percentage by which the population grows each decade.


c) Assuming that this rate of exponential growth continues, when will the global population reach 1010?


d) Assuming that this rate of exponential growth also applied before 1900, estimate what the global population was in the year 1800, to an appropriate number of significant figures
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old_engineer
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(Original post by John158)
Sorry I am still having problems understanding.

This is the full thing:

The global human population was approximately 1.6x10^9 in 1900, and 6.1x10^9 in 2000. The population dynamics can be modelled by the exponential growth formula Nt = N0e kt.

a) Using the above information, write a general expression for the rate constant k and then evaluate this expression to evaluate this constant to 3 significant figures (Use years as the unit of time).


b) Calculate the percentage by which the population grows each decade.


c) Assuming that this rate of exponential growth continues, when will the global population reach 1010?


d) Assuming that this rate of exponential growth also applied before 1900, estimate what the global population was in the year 1800, to an appropriate number of significant figures
What I posted in #3 applies to part (a). Can you do that bit?
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John158
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(Original post by old_engineer)
What I posted in #3 applies to part (a). Can you do that bit?
Yes but only while I was following along to a video so don't really understand how I can do it with this
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old_engineer
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(Original post by John158)
Yes but only while I was following along to a video so don't really understand how I can do it with this
First, are you happy that the two equations I posted in #3 represent the information given in the question for the years 1900 and 2000?
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John158
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(Original post by old_engineer)
The information given to you in the question is:

N_{1900}=1.6 \times 10^{9}=N_0e^{1900k}
N_{2000}=6.1 \times 10^{9}=N_0e^{2000k}

To find the value of k, you can divide one of those equations by the other (which eliminates N_0). Then to find the value of N_0 you can substitute your value for k into one of the equations above.
I think so, but does N0 = both these numbers or is one N0 and one Nt?
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old_engineer
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(Original post by John158)
I think so, but does N0 = both these numbers or is one N0 and one Nt?
N_0 is the same constant in both equations.

N_t=N_0e^{kt} is the general equation, where t is time in years (e.g. 1900 or 2000 etc), k is a constant to be found and N_0 is a constant to be found.

So, you have two equations and two unknowns....
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John158
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okay so I calculated
a) k = 0.134
b) = 2.812500 x 10^0 = 281.25%
c) 2000.176

Do I need to use one of these in it?
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old_engineer
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(Original post by John158)
okay so I calculated
a) k = 0.134
b) = 2.812500 x 10^0 = 281.25%
c) 2000.176

Do I need to use one of these in it?
a) looks to be out by a factor of 10;
b) likely to have been affected by (a)
c) likewise.

You can check your values for N0 and k by plugging them back into the equations for N1900 and N2000.
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John158
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(Original post by old_engineer)
a) looks to be out by a factor of 10;
b) likely to have been affected by (a)
c) likewise.

You can check your values for N0 and k by plugging them back into the equations for N1900 and N2000.
I re calculated it and it says a is 1.338285 x 10^2

I though b would be C=x1 - x2 / x1 = 6.1 x 1010 – 1.6 x 1010 / 1.6 x 1010 = 2.812500 x 100

2.812500 x 100/ 100 = 281.25 %


but this must not be the way to do it?
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old_engineer
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(Original post by John158)
I re calculated it and it says a is 1.338285 x 10^2

I though b would be C=x1 - x2 / x1 = 6.1 x 1010 – 1.6 x 1010 / 1.6 x 1010 = 2.812500 x 100

2.812500 x 100/ 100 = 281.25 %


but this must not be the way to do it?
a) Should be 1.34 x 10^(-2), not 1.34 x 10^2

b) Yes the ratio of N2000 / N1900 is 3.85, but these dates are 100 years apart rather than 10.
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John158
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(Original post by old_engineer)
a) Should be 1.34 x 10^(-2), not 1.34 x 10^2

b) Yes the ratio of N2000 / N1900 is 3.85, but these dates are 100 years apart rather than 10.
How would I write this for b?
also 1010 in my last post is meant to be 10^10
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old_engineer
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(Original post by John158)
How would I write this for b?
also 1010 in my last post is meant to be 10^10
Consider the ratio of the N values for two general years (p + 10) and p.
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John158
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(Original post by old_engineer)
Consider the ratio of the N values for two general years (p + 10) and p.
I dont think I understand what that means
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old_engineer
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(Original post by John158)
I dont think I understand what that means
Year p+10: N_{p+10}=N_0e^{k(p+10)}
Year p: N_{p}=N_0e^{kp}

These two years are ten years apart. You can find the ratio \frac{N_{p+10}}{N_p} and from that you can determine the percentage increase in population over the ten years.
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John158
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(Original post by old_engineer)
Year p+10: N_{p+10}=N_0e^{k(p+10)}
Year p: N_{p}=N_0e^{kp}

These two years are ten years apart. You can find the ratio \frac{N_{p+10}}{N_p} and from that you can determine the percentage increase in population over the ten years.

I'm getting confused going up and down so here it is again:

The global human population was approximately 1.6x109 in 1900, and 6.1x109 in 2000. The population dynamics can be modelled by the exponential growth formula Nt = N0e kt.

a) Using the above information, write a general expression for the rate constant k and then evaluate this expression to evaluate this constant to 3 significant figures (Use years as the unit of time).

=1.34 x 10^(-2)

b) Calculate the percentage by which the population grows each decade.

the years apart are 100 so is it still the same

so 6.1 x 109 + 10 / 1.6 x 109 ?
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old_engineer
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(Original post by John158)
I'm getting confused going up and down so here it is again:

The global human population was approximately 1.6x109 in 1900, and 6.1x109 in 2000. The population dynamics can be modelled by the exponential growth formula Nt = N0e kt.

a) Using the above information, write a general expression for the rate constant k and then evaluate this expression to evaluate this constant to 3 significant figures (Use years as the unit of time).

=1.34 x 10^(-2)

b) Calculate the percentage by which the population grows each decade.

the years apart are 100 so is it still the same

so 6.1 x 109 + 10 / 1.6 x 109 ?
"The years are 100 apart so it is still the same". Not sure what you mean by that. You are asked to find the % increase in population over 10 years, not over 100 years. They are not the same. I have suggested a method for ten years in post #17.
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John158
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(Original post by old_engineer)
"The years are 100 apart so it is still the same". Not sure what you mean by that. You are asked to find the % increase in population over 10 years, not over 100 years. They are not the same. I have suggested a method for ten years in post #17.
Sorry about that, I'm talking nonsense. My head is too sore to concentrate.

so using that it would be like above, 6.1 x 109 + 10 / 1.6 x 109
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