SOLUTION: The rat population in a major metropolitan city is given by the formula n(t)= 79 e^(0.015 t) where t is measured in years since 1992 and n(t) is measured in millions. What

Algebra ->  Functions -> SOLUTION: The rat population in a major metropolitan city is given by the formula n(t)= 79 e^(0.015 t) where t is measured in years since 1992 and n(t) is measured in millions. What      Log On


   



Question 976726: The rat population in a major metropolitan city is given by the formula n(t)= 79 e^(0.015 t) where t is measured in years since 1992 and n(t) is measured in millions.
What was the rat population in 1992 ?
What is the rat population going to be in the year 2009 ?

Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We are told that "t is measured in years since 1992". This means t = 0 corresponds to 1992. Plug in t = 0.

n(t)= 79*e^(0.015*t)
n(0)= 79*e^(0.015*0)
n(0)= 79*e^(0)
n(0)= 79*1
n(0)= 79

The population in 1992 is 79 million rats

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2009 - 1992 = 17

The value t = 17 corresponds to the year 2009. Plug in t = 17 to figure out the approximate population in 2009.

n(t)= 79*e^(0.015*t)
n(17)= 79*e^(0.015*17)
n(17)= 79*e^(0.255)
n(17)= 79*1.290461620873
n(17)= 101.946468048967
n(17)= 102

The population in 2009 is 102 million rats (approximate)
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+n%28t%29+=+79%2Ae%5E%28+.015t+%29+
+t+ is years since 1992
-----------------------
To show the year 1992, set
+t+=+0+
Any number to the zero power
is +1+
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+n%280%29+=+79%2Ae%5E0+
+n%280%29+=+79+
The rat population in 1992 was 79 million
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2009 is +17+ years since 1992
+n%2817%29+=+79%2Ae%5E%28+.015%2A17+%29+
+n%2817%29+=+79%2Ae%5E.255+
+n%2817%29+=+79%2A1.2905+
+n%2817%29+=+101.95+
The rat population in 2009 will be 101,949,500