John158
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Can anyone say what to do with c ?

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
= 0.0134 years

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


= 2.812500 x 100/ 100 = 281.25 % 281.25 / 10 = 2.812500 X10^1 = 28.125 %


c) Assuming that this rate of exponential growth continues, when will the global population reach 1010?
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old_engineer
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(Original post by John158)
Can anyone say what to do with c and d?

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
= 0.0134 years

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


= 2.812500 x 100/ 100 = 281.25 % 281.25 / 10 = 2.812500 X10^1 = 28.125 %


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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AUTHCENTRE
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(Original post by John158)
Can anyone say what to do with c ?

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
= 0.0134 years

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


= 2.812500 x 100/ 100 = 281.25 % 281.25 / 10 = 2.812500 X10^1 = 28.125 %


c) Assuming that this rate of exponential growth continues, when will the global population reach 1010?
c)
(1*10^10)/(1.6*10^9)=6.25
ln(6.25)/(1.34*10^-2)=136.7 years
1900+136.7=2036.7
d)
(1.6*10^9)*e^(0.0134t)=Pop in 1800 where t=-100 (As it is 100 years before 1900)
4.19*10^8 people in 1800
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davros
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(Original post by AUTHCENTRE)
c)
(1*10^10)/(1.6*10^9)=6.25
ln(6.25)/(1.34*10^-2)=136.7 years
1900+136.7=2036.7
d)
(1.6*10^9)*e^(0.0134t)=Pop in 1800 where t=-100 (As it is 100 years before 1900)
4.19*10^8 people in 1800
This is a duplicate thread, but please don't post full solutions in future - it's against the rules of the forum
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