You titled this "homework help" but are asking for someone to do the problem for you. That is NOT "help"!
Here is "help":
Do you understand what the problem is asking? You are given a formula with the variable "t". What does "t" represent? What does the problem say that formula tells you?
You are asked for the initial number of grasshoppers. What does "initial" mean? What value of t should you put in the formula?
You are asked for the "population of grasshopper after five weeks (both as an exact value and as a rounded value)" What value of t should you put in the formula for this? Do you understand the difference between "an exact value" and "a rounded value"?
You are asked to find the greatest number of grasshoppers and when it occurs. What is the greatest value of sin(x)? What value of x gives that greatest value?
You are asked when the number of grasshoppers will be 6000. Set that formula equal to 6000 and solve for t.
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