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 in T years after beginning his firm.

Answer 1

Write out the information given

`\begin{gathered} C=\text{Number of client in the first year} \\ T=\text{Number of years } \end{gathered}`

For the first year, the number of client is 36,

For the second year, the number of client is 44,

Since a linear trends continue, the sequence for the number of client will be

`36,44,52\ldots`

This form an arithematic sequence

Hence, for an arithemetic sequence, we have

`\begin{gathered} \text{For the first year, T=0} \\ C=\text{ 36} \\ \text{For the second year, T=1} \\ C=36+8(1)=36+8=44 \\ \text{For the third year, T=2} \\ C=36+8(2)=36+16=52 \end{gathered}`

Hence

In T years, we will have

`\begin{gathered} C=36+8(T) \\ \text{Then} \\ C=36+8T \end{gathered}`

Therefore

The equation that will yield the number of client C the lawyer will have in T years is

Answer : C = 36 + 8T