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.

I have no idea where to begin... Help.

Kathy/CeeCee -- Please do not switch names. It's unnecessary.

Thanks.

To determine if the limit of S exists as t approaches 2, we need to study the behavior of the salary over time. From the information given in the problem, we know that the salary increases by 10% every year for 3 years.

Let's analyze the salary progression year by year:

Year 0 to Year 1: The salary increases by 10% from $28.00, giving a new salary of $28.00 + 10% of $28.00 = $28.00 + $2.80 = $30.80.

Year 1 to Year 2: The salary increases by 10% from $30.80, giving a new salary of $30.80 + 10% of $30.80 = $30.80 + $3.08 = $33.88.

Year 2 to Year 3: The same pattern applies, with a 10% increase from $33.88, giving a new salary of $33.88 + 10% of $33.88 = $33.88 + $3.39 = $37.27.

However, the information given only provides the salary values for specific time intervals (0 < t < 1, 1 < t < 2, and 2 < t < 3). There is no specific value provided for t = 2.

To determine if the limit of S exists as t approaches 2, we would need the salary value for the time interval 2 < t < 3. Without that information, we cannot definitively conclude whether the limit exists.

In summary, based on the given information, we cannot determine if the limit of S exists as t approaches 2 since the salary value for the specific time interval of 2 < t < 3 is missing.