Question

The rise of digital video and the improvement to the DVD format are some of the reasons why the average selling price of stand-alone DVD recorders has dropped in recent years. The functionA(t) = 699(t + 1)0.94 (0 ≤ t ≤ 13)gives the projected average selling price (in dollars) of stand-alone DVD recorders in year t, where t = 0 corresponds to the beginning of 2002.† (Round your answers to the nearest cent.)How fast was the average selling price of stand-alone DVD recorders falling at the beginning of 2002?

Answer 1

A'(0) = 657.06

Step-by-step explanation:

`A_((t)) =699(t+1)^(0.94)`

To know the fall in prices on 2002 we need to calculate A't

to derivate a power, the current value the power multiplies and we subtract one from it:

As the base is a funtion we need to derivate that as well:

dt(t+1) = 1

`A_((t)) =699(0.94)* (t+1)^(0.94 - 1) * dt(t+1)`

`A_((t)) =657.06* (t+1)^(-0.06) * 1`

`(657.06)/((t+1)^(0.06))`

Know we calculate for t = 0

`(657.06)/((0+1)^(0.06))`

A'(0) = 657.06