# Growth formula

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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

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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#3

(Original post by

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

**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

To find the value of k, you can divide one of those equations by the other (which eliminates ). Then to find the value of you can substitute your value for k into one of the equations above.

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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

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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#5

(Original post by

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

**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

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(Original post by

What I posted in #3 applies to part (a). Can you do that bit?

**old_engineer**)What I posted in #3 applies to part (a). Can you do that bit?

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#7

(Original post by

Yes but only while I was following along to a video so don't really understand how I can do it with this

**John158**)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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(Original post by

The information given to you in the question is:

To find the value of k, you can divide one of those equations by the other (which eliminates ). Then to find the value of you can substitute your value for k into one of the equations above.

**old_engineer**)The information given to you in the question is:

To find the value of k, you can divide one of those equations by the other (which eliminates ). Then to find the value of you can substitute your value for k into one of the equations above.

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#9

(Original post by

I think so, but does N0 = both these numbers or is one N0 and one Nt?

**John158**)I think so, but does N0 = both these numbers or is one N0 and one Nt?

is the general equation, where is time in years (e.g. 1900 or 2000 etc), k is a constant to be found and is a constant to be found.

So, you have two equations and two unknowns....

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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?

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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#11

(Original post by

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?

**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?

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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(Original post by

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.

**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 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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#13

(Original post by

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?

**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?

b) Yes the ratio of N2000 / N1900 is 3.85, but these dates are 100 years apart rather than 10.

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(Original post by

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.

**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.

also 1010 in my last post is meant to be 10^10

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#15

(Original post by

How would I write this for b?

also 1010 in my last post is meant to be 10^10

**John158**)How would I write this for b?

also 1010 in my last post is meant to be 10^10

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(Original post by

Consider the ratio of the N values for two general years (p + 10) and p.

**old_engineer**)Consider the ratio of the N values for two general years (p + 10) and p.

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#17

(Original post by

I dont think I understand what that means

**John158**)I dont think I understand what that means

Year

These two years are ten years apart. You can find the ratio and from that you can determine the percentage increase in population over the ten years.

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(Original post by

Year

Year

These two years are ten years apart. You can find the ratio and from that you can determine the percentage increase in population over the ten years.

**old_engineer**)Year

Year

These two years are ten years apart. You can find the ratio 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 1.6x10

^{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).

=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 10

^{9}+ 10 / 1.6 x 10

^{9 }?

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#19

(Original post by

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

The global human population was approximately 1.6x10

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 10

**John158**)I'm getting confused going up and down so here it is again:

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).

=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 10

^{9}+ 10 / 1.6 x 10^{9 }?
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(Original post by

"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.

**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.

so using that it would be like above, 6.1 x 10

^{9}+ 10 / 1.6 x 10

^{9 }

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