C(t)=0.30-0.18[[-(t-1)]] (a) Use a graphing utilit

Questions: C(t)=0.30-0.18[[-(t-1)]] (a) Use a graphing utility to graph the cost function for 0<t ≤ 5. (b) Use the graph to complete the table below and observe the behavior of the function as t approaches 3.5 . t 3 3.3 3.4 3.5 3.6 3.7 4 C(t) Use the graph and the table to find the following limit. lim t → 3.5 C(t) (c) Use the graph to complete the table below and observe the behavior of the function as t approaches 3. t 2 2.5 2.9 3 3.1 3.5 4 C(t)

Transcript text: C(t)=0.30-0.18[[-(t-1)]] (a) Use a graphing utility to graph the cost function for $0

Solution

Solution Steps

Step 1: Evaluate C(t) for t values approaching 3.5 from the left.

Reading from the third graph provided, when _t_ = 3, C(t) = 1. When _t_ = 3.3, C(t) is between 0.5 and 1, but appears closer to 0.5 so we estimate C(3.3) = 0.6. When _t_ = 3.4, C(t) seems to be exactly 0.5.

Step 2: Evaluate C(t) for t values approaching 3.5 from the right.

From the graph, when _t_ = 4, C(t) = 0.12. When _t_ = 3.7, C(t) appears to be approximately 0.2. When _t_ = 3.6, C(t) appears to be slightly less than 0.3.

Step 3: Evaluate the limit as t approaches 3.5.

As _t_ approaches 3.5 from the left, C(t) appears to be approaching 0.5. As _t_ approaches 3.5 from the right, C(t) also appears to be approaching 0.5. Therefore, the limit of C(t) as _t_ approaches 3.5 is 0.5.

Final Answer:

The completed table for part (b) is:

| t | 3 | 3.3 | 3.4 | 3.5 | 3.6 | 3.7 | 4 | | :---- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | C(t) | 1 | 0.6 | 0.5 | 0.5 | 0.3 | 0.2 | 0.1 |

The limit of C(t) as t approaches 3.5 is 0.5.

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