Questions: The table shows the number of cars sold per month at Lemon cars where t is in weeks and S(t) is the number of cars sold. Find the average change in number of cars sold between weeks 2 and 5. t 1 2 3 4 5 6 S(t) 24 15 12 23 24 23 The average rate of change in the number of cars sold was by between weeks 2 and 5.

The table shows the number of cars sold per month at Lemon cars where t is in weeks and S(t) is the number of cars sold. Find the average change in number of cars sold between weeks 2 and 5.

t  1  2  3  4  5  6
S(t)  24  15  12  23  24  23

The average rate of change in the number of cars sold was by between weeks 2 and 5.
Transcript text: The table shows the number of cars sold per month at Lemon cars where $t$ is in weeks and $S(t)$ is the number of cars sold. Find the average change in number of cars sold between weeks 2 and 5 . \begin{tabular}{|c|c|c|c|c|c|c|} \hline$t$ & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline$S(t)$ & 24 & 15 & 12 & 23 & 24 & 23 \\ \hline \end{tabular} The average rate of change in the number of cars sold was $\square$ by $\square$ between weeks 2 and 5. Submit answer Next item
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Solution

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Solution Steps

To find the average change in the number of cars sold between weeks 2 and 5, we need to calculate the difference in the number of cars sold at these two points and then divide by the difference in time (weeks). Specifically, we use the formula for the average rate of change:

\[ \text{Average Rate of Change} = \frac{S(t_2) - S(t_1)}{t_2 - t_1} \]

where \( t_1 = 2 \) and \( t_2 = 5 \).

Step 1: Identify the Given Data

We are given the number of cars sold per week at Lemon Cars. The data is as follows: \[ \begin{array}{|c|c|c|c|c|c|c|} \hline t & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline S(t) & 24 & 15 & 12 & 23 & 24 & 23 \\ \hline \end{array} \]

Step 2: Determine the Values at Specific Weeks

We need to find the number of cars sold at weeks \( t_1 = 2 \) and \( t_2 = 5 \): \[ S(t_1) = 15, \quad S(t_2) = 24 \]

Step 3: Calculate the Average Rate of Change

The average rate of change in the number of cars sold between weeks 2 and 5 is given by: \[ \text{Average Rate of Change} = \frac{S(t_2) - S(t_1)}{t_2 - t_1} \] Substituting the values: \[ \text{Average Rate of Change} = \frac{24 - 15}{5 - 2} = \frac{9}{3} = 3.0 \]

Final Answer

\(\boxed{3}\)

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