SOLUTION: Can someone please help me solve this problem: In 2000 the population of a town was 35000. In 2010 it was 50000. Find an exponential model of the form f(t)=A base 0 e^kt for this p

Algebra ->  Functions -> SOLUTION: Can someone please help me solve this problem: In 2000 the population of a town was 35000. In 2010 it was 50000. Find an exponential model of the form f(t)=A base 0 e^kt for this p      Log On


   

Question 1082254: Can someone please help me solve this problem: In 2000 the population of a town was 35000. In 2010 it was 50000. Find an exponential model of the form f(t)=A base 0 e^kt for this population, where t is time in years since 2000. I also need help finding K but I think you have to use Ln logarithm but I am not sure.
Please and Thank you!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You are given 2 points in the form ( t, f(t) )
where +t+ is the time in years since 2000
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The points are:
( 0, 35000 )
( 10, 50000 )
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+f%28t%29+=+A%5B0%5D%2Ae%5E%28k%2At%29+
I can plug in the given points to
find +A%5B0%5D+ and +k+
---------------------------------
+35000+=+A%5B0%5D%2Ae%5E%28k%2A0%29+
+35000+=+A%5B0%5D%2A1+
+A%5B0%5D+=+35000+
and
+50000+=+A%5B0%5D%2Ae%5E%28k%2A10%29+
+50000+=+35000%2Ae%5E%28k%2A10%29+
+e%5E%2810k%29+=+10%2F7+
Take the natural log of both sides
+10k+=+ln%2810%29+-+ln%287%29+
+10k+=+2.3026+-+1.9459+
+10k+=+.3567+
+k+=+.03567+
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The equation is
+f%28t%29+=+35000%2Ae%5E%28+.03567t+%29+
check the math & get another
opinion if needed