Question

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).

Answer 1

`P'(t) = -10t + 75` and P'(5) = 25.

Explanation:

We are given that,

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

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

`P'(t) = -5*2t + 75`

i.e.
`P'(t) = -10t + 75`

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

`P'(5) = -10* 5+75`

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

i.e. P'(5) = 25

Hence, we get,

`P'(t) = -10t + 75` and P'(5) = 25.