contestada

The median home price in the United States over the period 2003-2011 can be approximated by P(t) = −5t2 + 75t − 30 thousand dollars (3 ≤ t ≤ 11), where t is time in years since the start of 2000.† Find P'(t) and P'(5).

Respuesta :

Answer:

[tex]P'(t) = -10t + 75[/tex] and P'(5) = 25.

Step-by-step explanation:

We are given that,

The median home price is represented by the function, [tex]P(t) = -5t^2 + 75t -30[/tex].

So, differentiating the function with respect to 't', we get,

[tex]P'(t) = -5\times2t + 75[/tex]

i.e. [tex]P'(t) = -10t + 75[/tex]

So, after subsituting 't=5', we get,

[tex]P'(5) = -10\times 5+75[/tex]

i.e. P'(5) = -50+75

i.e. P'(5) = 25

Hence, we get,

[tex]P'(t) = -10t + 75[/tex] and P'(5) = 25.

Otras preguntas