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Laura runs during her lunch break.
The average speed S, in kilometers per hour, at which Laura runs depends on the temperature t, in degrees Celsius (°C), at the start of her run and can be modeled by the function S(t) = 6 + 0.2(25 - t).

The distance, D, in kilometers, that she can run in 30 minutes given that her average speed is a kilometers per hour can be modeled by the function D(x) = 0.5x.

Which expression models the distance that Laura runs in 30 minutes given that it is t°C outside at the start of her run?

A. 5.5 - 0.2t
B. 11 - 0.1t
C. 11 - 0.5t
D. 5.5 - 0.1t



Answer :

Using composite functions, the expression that models the distance that she runs is:

D. 5.5 - 0.1t.

What is the composite function of f(x) and g(x)?

The composite function of f(x) and g(x) is given by:

(f ∘ g)(x) = f(g(x)).

In this problem, we have that:

  • The velocity as a function of the temperature is: S(t) = 6 + 0.2(25 - t) = 11 - 0.2t.
  • The distance as a function of the velocity is: D(x) = 0.5x.

Hence the distance as a function of the temperature is given as follows:

(D ∘ S)(t) = D(S(t)) = 0.5(11 - 0.2t) = 5.5 - 0.1t.

Which means that option D is correct.

More can be learned about composite functions at https://brainly.com/question/10687170

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