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
What function models the total number of visitors at both parks each hour after sunrise?
To find the total number of visitors at both parks each hour after sunrise, we need to add the number of visitors at each park together.
Let T(x) represent the total number of visitors at both parks each hour after sunrise.
We can determine T(x) by adding A(x) (the number of visitors at West Park) to B(x) (the number of visitors at East Park):
T(x) = A(x) + B(x)
T(x) = (-0.68x^3 + 7.05x^2 + 3.25x) + (-2.08x^2 + 22x + 5)
Simplifying the equation:
T(x) = -0.68x^3 + 7.05x^2 + 3.25x -2.08x^2 + 22x + 5
Combining like terms:
T(x) = -0.68x^3 + (7.05 - 2.08)x^2 + (3.25 + 22)x + 5
T(x) = -0.68x^3 + 4.97x^2 + 25.25x + 5
So the function that models the total number of visitors at both parks each hour after sunrise is:
T(x) = -0.68x^3 + 4.97x^2 + 25.25x + 5.