A submarine is diving toward the bottom of the ocean. The depth of the submarine, D, in feet below sea level, after t minutes have elapsed is given by the function D(t) 20+16t. The pressure, P, in pounds per square inch, exerted on the submarine at a depth of z feet is given by the function P(z) 14.7+0.445r Find an explicit expression that models the pressure exerted on the submarine as a function of the elapsed time, t, in minutes.

Respuesta :

Answer:

[tex]P(t) = 23.6+7.12t[/tex].

Step-by-step explanation:

The function [tex]D(t)[/tex] gives the depth as a function of time, and [tex]P(z)[/tex] gives the pressured exerted as a function of depth; therefore, the pressure exerted as a function of time will be modeled by the function [tex]P(x(t))[/tex] or [tex]P(D(t))[/tex]

Since [tex]D(t)= 20+16t[/tex],

[tex]P(D(t)) = 14.7+0.445(20+16t)[/tex]

[tex]P(D(t)) = 23.6+7.12t[/tex]

Therefore,

[tex]\boxed{P(t) = 23.6+7.12t.}[/tex]

Answer:

P(t) = 23.6 + 7.12t

Step-by-step explanation:

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