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:
[tex]f(t)=260ln(t)[/tex]
After two weeks (t=2), the revenue from sales is:
[tex]f(2)=260ln(2)\\f(2) = \$180.22[/tex]
The rate of change, which is given by the derivate of the revenue function, at t = 2 weeks is:
[tex]f'(t)=\frac{d}{dt} 260ln(t)\\f'(t) = \frac{260}{t}\\f'(2) = \frac{260}{2}=\$130.00/week[/tex]
The relative rate of change is:
[tex]\frac{f'(2)}{f(2)}=\frac{130}{180.22}=0.7213=72.13\%[/tex]
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.
