Question

Jack is performing an experiment in a laboratory. The resulting rise in temperature, t(x), of the chemical under observation, over time x, in hours, for the first ten hours can be modeled by a cubic function. Each of the following functions is a different form of the cubic model for the situation given above. Which form would be most helpful if attempting to determine the time at which the temperature is approximately constant?

t(x) = 0.05x(x2 - 15x + 75) + 43.75

t(x) = 0.05(x - 5)3 + 50

t(x) = 0.05(x3 - 15x2 + 75x + 875)

t(x) = 0.05x3 - 0.75x2 + 3.75x + 43.75

Answer 1

I'd say option D because you can just tell right off the bat that if x = 0, then f(x) = 43.75.

Answer 2

t(x)= 0.05(x-5)^3+50

Explanation:

Since the balance point in a cubic function appears on the line of symmetry, it is the vertex itself. A translation h units to the right and k units up of a cubic function, which has the vertex at the origin, can be represented by the function in the following form, where (h,k) is the vertex of the function.