Question

Rodrigo is tracking the number of visitors at two parks. He created these functions to model the total number of people visiting each park, where x is the number of hours after sunrise.

West Park: A(X) = -0.68x^3 + 7.05x^2 + 3.25x
East Park: B(x) = -2.08x^2 +22x+ 5

Which function models the total number of visitors at both parks each hour after sunrise?

A T(x) = -0.68x^3 + 9.13x^2 + 22x + 8.25
B. T(x) = -0.68x^3 + 4.97x^2 + 25.25x + 5
C. T(x) = -2.76x^3 + 7.05x^2 + 25.25x + 5
D. T(x) = -2.76x^3 + 29.05x^2 + 8.25

Answer 1

Answer: For plato family

B. T(x) = -0.68x^3 + 4.97x^2 + 25.25x + 5

Explanation:

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Answer 2

The function that models the total number of visitors at both parks each hour after sunrise:
`\mathbf{T(x) = -0.68x^3 + 4.97x^2 + 25.25x + 5}`

Option B is correct.

Explanation:

Function for West Park: A(X) =
`-0.68x^3 + 7.05x^2 + 3.25x`

Function for East Park: B(x) =
`-2.08x^2 +22x+ 5`

We need to find the function that models the total number of visitors at both parks each hour after sunrise?

For finding total number of visitors we need to sum functions of A(X) and B(X) to get T(X)

So, we have

`T(X)=A(X)+B(X)\\T(X)=-0.68x^3 + 7.05x^2 + 3.25x+(-2.08x^2 +22x+ 5)\\T(X)=-0.68x^3 + 7.05x^2 + 3.25x-2.08x^2 +22x+ 5\\Combining like terms\\T(X)=-0.68x^3+7.05x^2-2.08x^2+3.25x+22x+5\\T(X)=-0.68x^3+4.97x^2+25.25x+5`

So, function that models the total number of visitors at both parks each hour after sunrise:
`\mathbf{T(x) = -0.68x^3 + 4.97x^2 + 25.25x + 5}`

Option B is correct.