On a camping trip with friends, you read about mosquito activity after dark. the number of mosquitos in your campground can be modeled using the function g(x) = x4 + 6x2 + 2x − 11, where x is the number of hours after sunset. you go out to build a campfire 3 hours after sunset. how many mosquitos are in your campground?
a) 0
b) 54
c) 66
d) 130

There are 130 mosquitoes in your campground ⇒ answer D

Step-by-step explanation:

* Lets explain how to solve the problem

-  The number of mosquitoes in the campground can be modeled

  using the function g(x) = x^4 + 6x² + 2x − 11

- The number of hours after sunset is x

- You go out to build a campfire 3 hours after sunset

- To find the number of mosquitoes substitute x by 3

* Lets solve the problem

∵ g(x) represents the number of mosquitoes in the campground

∵ g(x) = x^4 + 6x² + 2x - 11

∵ x is the number of hours after the sunset

∵ You want to know the number of mosquitoes after 3 hours

   from the sunset

- Substitute x by 3 in g(x)

∴ g(3) = (3)^4 + 6(3)² + 2(3) - 11

∴ g(3) = 81 + 6(9) + 6 -11

∴ g(3) = 81 + 54 + 6 - 11

∴ g(3) = 130

∴ The number of mosquitoes after 3 hours from sunset is 130

* There are 130 mosquitoes in your campground

D) 130

Step-by-step explanation:

Given : The number of mosquitoes in your campground can be modeled using the function , where x is the number of hours after sunset.

For x= 3

The number of mosquitoes in your campground 3 hours after sunset ,will be

Simplify ,

Therefore, there are 130 mosquitoes in your campground .

Hence, the correct options is D) 130

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