Suppose the rental cost for a snowboard is $25 for the first day (or any part of the first day) plus $15 for each additional day (or any part of a day).
e. For what values of t is f continuous? Explain.

Verified step by step guidance

1. Step 1: Understand the function f(t) that represents the rental cost. The function is piecewise, with a fixed cost for the first day and a different rate for additional days.
2. Step 2: Define the function f(t) as f(t) = 25 for 0 < t ≤ 1 and f(t) = 25 + 15(t - 1) for t > 1, where t is the number of days.
3. Step 3: Identify the points where the function might be discontinuous. Discontinuities in piecewise functions often occur at the boundaries between pieces, in this case, at t = 1.
4. Step 4: Check the continuity at t = 1 by evaluating the left-hand limit, right-hand limit, and the value of the function at t = 1. Ensure that these three values are equal for continuity.
5. Step 5: Conclude that the function f(t) is continuous for all t > 0 except possibly at t = 1, depending on the results of the limits and function value at that point.