SOLUTION: The population P(t) of a British Columbian town is modelled by the function P(t)=2t^2+80t+4000. Note: t=0 corresponds to the year 2000.When will the population double its current t

Algebra ->  Functions -> SOLUTION: The population P(t) of a British Columbian town is modelled by the function P(t)=2t^2+80t+4000. Note: t=0 corresponds to the year 2000.When will the population double its current t      Log On


   

Question 1030293: The population P(t) of a British Columbian town is modelled by the function P(t)=2t^2+80t+4000. Note: t=0 corresponds to the year 2000.When will the population double its current total? Explain how you got your answer.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+P%28t%29+=+2t%5E2+%2B+80t+%2B+4000+
+t+=+0+
+P%280%29+=+2%2A0%5E2+%2B+80%2A0+%2B+4000+
+P%280%29+=+4000+
+2%2A4000+=+8000+
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When does the population = +8000+ ?
+P%28t%29+=+8000+
+8000+=+2t%5E2+%2B+80t+%2B+4000+
+2t%5E2+%2B+80t+=+4000+
+t%5E2+%2B+40t+=+2000+
Complete the square
+t%5E2+%2B+40t+%2B+%28+40%2F2+%29%5E2+=+2000+%2B+%28+40%2F2+%29%5E2+
+t%5E2+%2B+40t+%2B+400+=+2000+%2B+400+
+%28+t+%2B+20+%29%5E2+=+2400+
+t+%2B+20+=+10%2Asqrt%2824%29+
+t+=+10%2A4.899+-+20+
+t+=+48.99+-+20+
+t+=+29+
Population will be double in 2029
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check:
+8000+=+2t%5E2+%2B+80t+%2B+4000+
+8000+=+2%2A29%5E2+%2B+80%2A29+%2B+4000+
+8000+=+1682+%2B+2320+%2B+4000+
+4000+=+4002+
Error due to rounding off?
I think so