SOLUTION: The population N(t) (in millions) of India t years after 1985 may be approximated by the formula N(t) = 766e^0.0182t. When will the population reach 1.4 billion? (Round your an

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Question 1007371: The population N(t) (in millions) of India t years after 1985 may be approximated by the formula
N(t) = 766e^0.0182t.
When will the population reach 1.4 billion? (Round your answer to one decimal place.)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

N(t) is the population in millions.
So if N(t) = 1, then we have 1 million people. If N(t) = 2, then we have 2 million, etc.
1.4 billion = 1400 million

So if N(t) is in millions, then N(t) = 1400 represents 1.4 billion people.

This means that we need to solve N(t) = 1400 for t

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N%28t%29+=+1400

766e%5E%280.0182t%29+=+1400

%28766e%5E%280.0182t%29%29%2F766+=+1400%2F766

e%5E%280.0182t%29+=+1400%2F766

Ln%28e%5E%280.0182t%29%29+=+Ln%281400%2F766%29

0.0182t%2ALn%28e%29+=+Ln%281400%2F766%29

0.0182t%2A1+=+Ln%281400%2F766%29

0.0182t+=+Ln%281400%2F766%29

%281%2F0.0182%29%2A0.0182t+=+%281%2F0.0182%29%2ALn%281400%2F766%29

t+=+%281%2F0.0182%29%2ALn%281400%2F766%29

t+=+33.134359662789

t+=+33.1

The population will reach 1.4 billion people after 33.1 years. This will happen between the years 2018 and 2019
Note: 1985+33 = 2018