Chapter 4.4, Problem 96E

(a)

To determine

To calculate: The value of $q^{\prime }\left(2\right)$ using technology where the equation for the amount of information that is transmitted every month in the early years of Internet from $1988-1994$ is $q\left(t\right)=\frac{2e^{0.69t}}{3+1.5e^{-0.4t}}\left(0\le t\le 6\right)$ where $q\left(t\right)$ is total amount of information transmitted in billions of data packets and t is time in years since $1988$.

(b)

To determine

To calculate: The marginal cost $C^{\prime }\left(q\right)$ if the cost for transmitting a million packets of data is $\$5$ and the equation for the amount of information that is transmitted every month in the early years of Internet from $1988-1994$ is $q\left(t\right)=\frac{2e^{0.69t}}{3+1.5e^{-0.4t}}\left(0\le t\le 6\right)$ where $q\left(t\right)$ is total amount of information transmitted in billions of data packets and t is time in years since $1988$.

(c)

To determine

To calculate: The rate at which cost is increasing at the start of $1990$ where the equation for the amount of information that is transmitted every month in the early years of Internet from $1988-1994$ is $q\left(t\right)=\frac{2e^{0.69t}}{3+1.5e^{-0.4t}}\left(0\le t\le 6\right)$ where $q\left(t\right)$ is total amount of information transmitted in billions of data packets and t is time in years since $1988$.