Question

The salary of members of two governing bodies in 2008 was ​$

Answer 1

Complete Question

The salary of members of two governing bodies in 2008 was $167.2 thousand, and has increased by approximately $2 thousand per year since then. Complete parts (a) and (b).

(a) Complete the following table to help find an expression that stands for the the salary (in thousands of dollars) of members of the two governing bodies t years since 2008.

Number of years and salaries of members of the two governing bodies

$\left|\begin{array}{c|c}-------&------\\ Years since 2008& Salary (thousands of dollars)\\-------&------\\0&(2*--) + --\\1&(2*--) + --\\2&(2*--) + --\\3&(2*--) + --\\4&(2*--) + --\\t&(2*--) + --\end{array}\right|$

(b) Evaluate the expression that is found in part (a) for t = 5. What does the result means in this situation?

Answer:

(a) $S(t)=2t+167.2$

(b) S(5)=$177.2 thousand.

Step-by-step explanation:

(a)

The salary increases by $2 thousand per year since 2008. Therefore, the completed table is below:

$\left|\begin{array}{c|c}-------&------\\ Years since 2008& Salary (thousands of dollars)\\-------&------\\0&(2\cdot 0) + 167.2\\1&(2\cdot 1) + 167.2\\2&(2\cdot 2) + 167.2\\3&(2\cdot 3) + 167.2\\4&(2\cdot 4) + 167.2\\t&(2\cdot t) + 167.2\end{array}\right|$

Therefore, an expression that gives the salary (in thousands of dollars) of members of the two governing bodies t years since 2008 is:

$S(t)=2t+167.2$

(b)

When t=5

$S(5)=2*5+167.2\\S(5)=177.2$

This means that 5 years after 2008 (i.e Year 2013) the salary of members of the two governing bodies will be approximately $177.2 thousand.