SOLUTION: Please help The population of India is 1.13 billion people and is expected to double in 36 years. The population of China is 1.32 billion people and is expected to double in 67

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Please help The population of India is 1.13 billion people and is expected to double in 36 years. The population of China is 1.32 billion people and is expected to double in 67       Log On


   

Question 331896: Please help
The population of India is 1.13 billion people and is expected to double in 36 years. The population of China is 1.32 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?
thanks
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
The population of India is 1.13 billion people and is expected to double in 36 years. The population of China is 1.32 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?
.
You will be applying the "exponential growth" formula:
N = Noe^(rt)
where
N = population at time t
No = initial population
r = constant (this what we need to find for India and China)
t = time
.
India:
2(1.13) = 1.13e^(r*36)
2 = e^(r*36)
ln(2) = r*36
ln(2)/36 = r
Equation of growth for India:
N = 1.13e^(ln(2)t/36)
.
China:
2(1.32) = 1.32e^(r*67)
2 = e^(r*67)
ln(2) = r*67
ln(2)/67 = r
Equation of growth for China:
N = 1.32e^(ln(2)t/67)
.
Set them equal and solve for t:
1.13e^(ln(2)t/36) = 1.32e^(ln(2)t/67)
take the ln of both sides:
ln(1.13e^(ln(2)t/36)) = ln(1.32e^(ln(2)t/67))
ln(1.13) + ln(2)t/36) = ln(1.32) + ln(2)t/67)
ln(2)t/36) - ln(2)t/67) = ln(1.32) - ln(1.13)
t(ln(2)/36) - ln(2)/67) = ln(1.32) - ln(1.13)
t = (ln(1.32)-ln(1.13))/(ln(2)/36) - ln(2)/67)
t = 17.45 years