Salary Contracy - A union contract guarantees a 10% salary increase yearly for 3 years. For a current salary of $28.00, the salary S (in thousands of dollars) for the next 3 years is given by...

S(t)=
28.00, 0<t<1
30.80, 1<t<2
33.88, 2<t<3
where t=0 represents the present year. Does the limit of S exist as t approaches 2? Explain your reasoning.

To determine if the limit of S exists as t approaches 2, we first need to find the values of S as t approaches 2 from both the left and right sides.

The given function S(t) is defined for specific ranges of t. We can plug in t=2 into the function and find the values of S(t) for t values close to 2 to see if they converge to a specific value.

For t values approaching 2 from the left side (t < 2), we can observe that as t gets closer to 2, the value of S(t) approaches 30.80. As t approaches 2 from the right side (t > 2), we can see that as t gets closer to 2, the value of S(t) approaches 33.88.

Since the values of S(t) approach different values as t approaches 2 from different sides, we can conclude that the limit of S does not exist as t approaches 2.

In this case, the lack of a limit suggests that the salary increase is discontinuous at t=2. It means that there is a jump in salary between the second and third years, which is likely due to the terms of the union contract.