Question

INTERNET A Webmaster estimates that the time (seconds) required to connect to the server when $\mathbf{n}$ people are connecting is given by $\mathbf{t}\left(\mathbf{n}\right)=\mathbf{0}.\mathbf{005}\mathbf{n}+\mathbf{0}.\mathbf{3}$. Estimate the time required to connect when 50 people are connecting. (Lesson 2-2)

Short answer

The time required to connect when 50 people are connecting is estimated to be 0.55 seconds.

Step-by-step solution

– State the concept

The value of $t\left(a\right)$ is obtained by putting $n=a$ in the expression for $t\left(n\right)$.

– List the given data

The time (in seconds) required to connect to the server when $n$ people are connecting is given by $t\left(n\right)=0.005n+0.3$.

– Evaluate the objective

The objective is to estimate the time required to connect when 50 people are connecting.

Then, in this case, $n=50$.

Put $n=50$in $t\left(n\right)=0.005n+0.3$to get,

$\begin{array}{l}t\left(50\right)=0.005\left(50\right)+0.3\\ =0.25+0.3\\ =0.55\end{array}$

So, $t\left(50\right)=0.55$

This implies that the time required to connect when 50 people are connecting is estimated to be 0.55 seconds.