Question

During the first year of opening his law firm a lawyer served 36 clients. In the second year his number of clients grew to 44. If a linear trend continues write an equation that gives the number of clients c the lawyer will have t years after beginning his firm

Answer 1

Given:

During the first year of opening his law firm, a lawyer served 36 clients.

In the second year, his number of clients grew to 44.

Let the number of clients = c, and the number of years = t

There is a linear relationship between c and t

We will find the equation that relates (c) and (t)

So, when t = 1, c = 36

and when t = 2, c = 44

The equation will take the general slope-intercept form

c = m * t + b

Where m is the slope, and b is the y-intercept

The slope will be calculated as follows:

$m=\frac{44-36}{2-1}=\frac{8}{1}=8$

So, the equation will be: c = 8t + b

using the first condition to find (b)

$\begin{gathered} 36=8\cdot1+b \\ b=36-8=28 \end{gathered}$

So, the answer will be the equation will be:

$c=8t+28$