Hi, My problem reads: The population of ducks in a pond can be modelled by the equation: P = 4 + 3sin(πt/3) Where is P = population in hundreds, and t = months. a. What is the population in April (P = 4) b. For how long during the year is he population above 600. I understand that you substitute the 4 into (t) in part a and 600 into (P), but am unsure how to solve.
+129820 Have a look at the graph here [I've substituted "y" for "P"....but it's the same idea] .....[note that we want P to just equal 6, not 600.....it's in hundreds ]
https://www.desmos.com/calculator/khtbnpjmhk
Notice that the poulation is greater than 6 from about .697months to about 2.303 months...or about 1.6 months....and the same time period occurs again from about 6.697 months to about 8.303 months
So....the total time that the population is greater than 6 is about 2(1.6) = about 3.2 months
+129820 Have a look at the graph here [I've substituted "y" for "P"....but it's the same idea] .....[note that we want P to just equal 6, not 600.....it's in hundreds ]
https://www.desmos.com/calculator/khtbnpjmhk
Notice that the poulation is greater than 6 from about .697months to about 2.303 months...or about 1.6 months....and the same time period occurs again from about 6.697 months to about 8.303 months
So....the total time that the population is greater than 6 is about 2(1.6) = about 3.2 months
