Question

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

Answer 1

Answer: D) 130

Explanation:

Given : The number of mosquitoes in your campground can be modeled using the function
`g(x) = x^4 + 6x^2 + 2x -11` , 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

`g(3) = (3)^4 + 6(3)^2 + 2(3) -11`

Simplify ,

`g(3) =81 + 6(9) + 6-11`

`\Rightarrow\ g(3) =81 + 54 -5=130`

Therefore, there are 130 mosquitoes in your campground .

Hence, the correct options is D) 130

Answer 2

There are 130 mosquitoes in your campground ⇒ answer D

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