Final answer:
Without specific information about the function's behavior at t=8, we cannot definitively determine if it is continuous at that point. The function is continuous if there is a smooth curve with no jumps or sharp bends at t=8, which would be aligned with answer options A and C. However, we need additional context or a graph of the function to make an accurate selection.
Step-by-step explanation:
To determine if the function n is continuous at t = 8, we evaluate the behavior of the function at that point. A function is continuous at a point if, roughly speaking, you can draw the function at that point without lifting the pencil from the paper. This includes the function being defined at the point, having a limit that exists at that point, and the limit equaling the function's value at that point. From the options provided, the correct determination depends on the specific characteristics of the function at t = 8.
However, from the provided information, we cannot definitively select an answer because we lack a description or graph of the function's actual behavior at t = 8. The references given talk about the slope of a tangent line and other properties, but they do not give specifics about the behavior at t = 8. Therefore, without additional context or a visualization of the graph, any choice made would be speculative.
If t = 8 coincides with information provided, such as a smooth curve or a sharp bend, we would then select the option that appropriately describes the scenario. For example, if t = 8 had a smooth curve with no jumps or discontinuities, the function would be continuous, justifying answer A or C. Conversely, if there was a sharp bend or sudden change in the slope, it may indicate a discontinuity, which might lead to answer B or D being correct.