Posted by **Leanna** on Sunday, August 29, 2010 at 1:49pm.

In 1951, the population of India was 357 million people. By 1981 it had grown to 984 million. If the population is growing exponentially, when (in what month of what year) will the population reach 1 billion people?

- Math AP Calc -
**Reiny**, Sunday, August 29, 2010 at 6:59pm
let the equation be

P = 357(e)^(kt) where t is the time in years since 1951

so 1981 ---> t = 30

984 = 357(e^30k)

2.756303 = e^30k

30k = ln 2.756303

k = .0337963

so now we have P = 357(e^.0337963t)

so 1000 = 357(e^.0337963t)

2.80112 = e^.0337963t

t = 30.477

30 years + .477 of the next year

30 yrs + 5.7 months

or

in the 6th month of 1951

- Math AP Calc -
**Leanna**, Sunday, August 29, 2010 at 7:33pm
wouldn't it be past 1981 instead of in the 6th month of 1951?

- Math AP Calc -
**Reiny**, Sunday, August 29, 2010 at 7:38pm
of course, clearly a typo. Sorry about that.

since my t=30.477 and I defined as 1951 as t=0

the time is 1951 + 30.477 = 1981 + .477yrs.

- Math AP Calc -
**Leanna**, Sunday, August 29, 2010 at 8:30pm
Does the .477 years mean the 6th month (June) you were talking about?

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