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The population of a city is 7 million, with exponential growth rate 4%. In how many years will
the population double in size?
Solution
genral exponential growth equation is P(t)=(P(0))ert
here population P(t) is in millions
The population of a city is 7 million =>P(0)=7
exponential growth rate 4% => r =4/100=0.04
population double =>P(t)=2*7=14 million
P(t)=(P(0))ert
=>14=7*e0.04t
=>e0.04t =(14/7)
=>e0.04t =2
=>0.04t =ln(2)
=>t=(1/0.04)ln(2)
=>t=17.33 years
so population doubles in size in 17.33 years approximately
please rate if helpful. please comment if you have any doubt

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The population of a city is 7 million, with exponential growth rate .pdf

  • 1. The population of a city is 7 million, with exponential growth rate 4%. In how many years will the population double in size? Solution genral exponential growth equation is P(t)=(P(0))ert here population P(t) is in millions The population of a city is 7 million =>P(0)=7 exponential growth rate 4% => r =4/100=0.04 population double =>P(t)=2*7=14 million P(t)=(P(0))ert =>14=7*e0.04t =>e0.04t =(14/7) =>e0.04t =2 =>0.04t =ln(2) =>t=(1/0.04)ln(2) =>t=17.33 years so population doubles in size in 17.33 years approximately please rate if helpful. please comment if you have any doubt