SOLUTION: An insect population P in a certain area fluctuates with the seasons. It is estimated that P = 17,000+ 4500sin πt/52, where t is given in weeks. Determine the number of week

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Question 42459: An insect population P in a certain area fluctuates with the seasons. It is estimated that P = 17,000+ 4500sin πt/52, where t is given in weeks. Determine the number of weeks it would take for the population to initially reach 20,000.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
P+=+17000+%2B+4500+%2A+sin%28pi%2At%2F52%29
P = 20000
20000+=+17000+%2B+4500+%2A+sin%28pi%2At%2F52%29
3000+=+4500+%2A+sin%28pi%2At%2F52%29
2+=+3+%2A+sin%28pi%2At%2F52%29
+sin%28pi%2At%2F52%29+=+2%2F3
arcsin%282%2F3%29+=+.7297
.7297+=+pi%2At%2F52
37.948+=+3.141+%2A+t
t+=+37.948+%2F+3.141
t+=+12.08
t = about 12 weeks