Expert: Sherman D. - 4/9/2006

Question
A few more questions that I need assistance with.

Directions:  India is currently one of the world's fastest-growing countries.  By 2040, the population of India will be larger than the population of China, by 2050, nearly one-third of the world's population will lives in these two countries alone.  The exponential growth model A = 574e^0.026t describes the population of India, A, in millions, t years after 1974.  Use this model to solve this exercise.

1)  When will India's population be 2732 million?

Directions:  Use the formula t= In 2/k that gives the time for a population with a growth rate k to double to solve this problem:  (express each answer to the nearest whole number)

2)  Japan is growing at a rate of 0.03% per year.  How long will it take Japan to double its population?

Answer
A = 574e^.026t

1.)
2732 = 574e^(.026t)
(2732/574) = e^(.026t)
ln(2732/574) = .026t
t = (ln(2732/574))/(.026)
t = (ln(2732/574))/(26/1000)
t = (ln(2732/574))/(13/500)
t = (500 * ln(2732/574))/13
t = about 60.01 years later

ANS : India's Popluation will be 2732 million in the year 2034

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If i understand you correctly

2.)
t = (ln(2))/(.03/100)
t = (ln(2))/(3/10000)
t = (10000 * ln(2))/3
t = 2310 years