A union contract guarantees a $15 \%$ salary increase yearly for 3 years. For a current salary of $\$ 31,000$, the salary $f ( t )$ (in thousands of dollars) for the next 3 years is given by
$$f ( t ) = \left\{ \begin{array} { l l }
31.00 , & 0

Question

A union contract guarantees a $15 \%$ salary increase yearly for 3 years. For a current salary of $\$ 31,000$, the salary $f ( t )$ (in thousands of dollars) for the next 3 years is given by
$$f ( t ) = \left\{ \begin{array} { l l } 
31.00 , & 0 < t \leq 1 \
35.65 , & 1 < t \leq 2 \
41.00 , & 2 < t \leq 3
\end{array} \right.$$
where $t$ represents the time in years. Find the limit of $f$ as $t \rightarrow 1.00$, if it exists.
A) $31.00$
B) $35.65$
C) $1.00$
D) $41.00$
E) The limit does not exist.

Quizplus · Accepted Answer

The limit does not exist because the function $f(t)$ has a jump discontinuity at $t = 1$. The left-hand limit as $t$ approaches 1 is 31.00, and the right-hand limit is 35.65, which are not equal.

A Union Contract Guarantees A 15%15 \%15% Salary Increase Yearly for 3 Years

A Union Contract Guarantees A $15 \%$ Salary Increase Yearly for 3 Years