SOLUTION
Write out the information given
[tex]\begin{gathered} C=\text{Number of client in the first year} \\ T=\text{Number of years } \end{gathered}[/tex]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
[tex]36,44,52\ldots[/tex]This form an arithematic sequence
Hence, for an arithemetic sequence, we have
[tex]\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}[/tex]Hence
In T years, we will have
[tex]\begin{gathered} C=36+8(T) \\ \text{Then} \\ C=36+8T \end{gathered}[/tex]Therefore
The equation that will yield the number of client C the lawyer will have in T years is
Answer : C = 36 + 8T
