SOLUTION: An insect population P in a certain area fluctuates with the seasons. It is estimated that P=17,000 + 4500sin(piT)/52, where T is given in weeks. Determine the number of weeks it w

Algebra ->  Trigonometry-basics -> SOLUTION: An insect population P in a certain area fluctuates with the seasons. It is estimated that P=17,000 + 4500sin(piT)/52, where T is given in weeks. Determine the number of weeks it w      Log On


   

Question 350612: An insect population P in a certain area fluctuates with the seasons. It is estimated that P=17,000 + 4500sin(piT)/52, where T is given in weeks. Determine the number of weeks it would take for the population to initially reach 20,000?
A.) 12 weeks
B.) 692 weeks
C.) 38 weeks
D.) 42 weeks
I don't understand how I would go about solving this so any help is appreciated! Thank You!!!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You have an equation that gives you an output of P with a given input T.
You're given P and need to find T.
Use the equation.
P=17000+%2B+4500sin%28%28pi%2AT%29%2F52%29
20000=17000%2B4500sin%28%28pi%2AT%29%2F52%29
4500sin%28%28pi%2AT%29%2F52%29=3000
sin%28%28pi%2AT%29%2F52%29=2%2F3
Find the angle (in radians) whose sine is 2/3.
%28pi%2AT%29%2F52=0.7297
Now solve for T.