Question 422462: The population of India is 1.17 billion people and is expected to double in 44 years. The population of China is 1.34 billion people and is expected to double in 67 years. If the trends continue, when will the population of India be the same as China's?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! The population of India is 1.17 billion people and is expected to double in 44 years. The population of China is 1.34 billion people and is expected to double in 67 years. If the trends continue, when will the population of India be the same as China's?
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The formula for population growth:
N(t)=Noe^kt
N(t)=population after t years
No=current population
k=growth constant
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finding growth constant using given data and doubling time formula.
doubling time,T=ln2/k
k=ln2/T
for China
k1=ln2/67
N(t)=1.34e^k1t
for India
k2=ln2/44
N(t)=1.17e^k2t
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1.34e^k1t=1.17e^k2t
taking logarithms of both sides,
ln(1.34)+k1t(ln(e))=ln(1.17)+k2t(ln(e))
ln(1.34)+k1t=ln(1.17)+k2t
ln(1.34)-ln(1.17)=k2t-k1t=t(k2-k1)
t=ln(1.34)-ln(1.17)/(k2-k1)
t=25.09 years
ans:
The population of India will be the same as that of China in apprximately 25 years.
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