Question

A new DVD is available for sale in a store one week after its release. The cumulative revenue,

Answer 1

Answer:

f(2) = $180.22

f'(2) = $130.00/week

f'(2)/f(2) = 72.13%

Two weeks after the DVD was released,  the revenue from sales is $180.22 and is increasing at a rate of $130 per week,  or 72.13% per week.

Step-by-step explanation:

The revenue from sales, in dollars, as a function of time, in weeks, is given by:

$f(t)=260ln(t)$

After two weeks (t=2), the revenue from sales is:

$f(2)=260ln(2)\\f(2) = \ 180.22$

The rate of change, which is given by the derivate of the revenue function, at t = 2 weeks is:

$f'(t)=\frac{d}{dt} 260ln(t)\\f'(t) = \frac{260}{t}\\f'(2) = \frac{260}{2}=\ 130.00/week$

The relative rate of change is:

$\frac{f'(2)}{f(2)}=\frac{130}{180.22}=0.7213=72.13\%$

Therefore, Two weeks after the DVD was released,  the revenue from sales is $180.22 and is increasing at a rate of $130 per week,  or 72.13% per week.