A union contract guarantees a $16 \%$ salary increase yearly for 3 years. For a current salary of $\$ 31,500$, the salary $f ( t )$ (in thousands of dollars) for the next 3 years is given by
$$f ( t ) = \left\{ \begin{array} { l l }
31.50 , & 0

Question

A union contract guarantees a $16 \%$ salary increase yearly for 3 years. For a current salary of $\$ 31,500$, the salary $f ( t )$ (in thousands of dollars) for the next 3 years is given by
$$f ( t ) = \left\{ \begin{array} { l l } 
31.50 , & 0 < t \leq 1 \
36.54 , & 1 < t \leq 2 \
42.39 , & 2 < t \leq 3
\end{array} \right.$$
where $t$ represents the time in years. Find the limit of $f$ as $t \rightarrow 1.00$, if it exists.
A) $31.50$
B) $36.54$
C) $1.00$
D) $42.39$
E) The limit does not exist.

Quizplus · Accepted Answer

The limit does not exist because the function $f(t)$ has a jump discontinuity at $t = 1$, with different values on either side of $t = 1$.

A Union Contract Guarantees A 16%16 \%16% Salary Increase Yearly for 3 Years

A Union Contract Guarantees A $16 \%$ Salary Increase Yearly for 3 Years