Question

The graph shows the number of computers assembled during each of 6 consecutive days. From what day to the next day was the percent change in the number of computers assembled the greatest in magnitude?

• A. From Day 1 to Day 2
• B. From Day 2 to Day 3
• C. From Day 3 to Day 4
• D. From Day 4 to Day 5
• E. From Day 5 to Day 6

Hint:

When calculating percent change, the "from" value (the earlier day) is always the denominator. A large absolute change from a small starting value will result in a large percent change. You can often estimate visually: the jump from 10 to 16 is a change of 6, which is more than half of the starting value of 10, indicating a percent change greater than 50%.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The question asks for the greatest "percent change in magnitude." This means we need to calculate the percent change for each consecutive pair of days and then find the largest absolute value (ignoring any negative signs).
Step 2: Key Formula or Approach:
The formula for percent change is:
\[ \text{Percent Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100% \] We will first read the values from the bar chart and then apply this formula to each option.
Step 3: Detailed Explanation:
First, let's list the number of computers assembled each day from the graph:
- Day 1: 20
- Day 2: 12
- Day 3: 18
- Day 4: 10
- Day 5: 16
- Day 6: 8
Now, we calculate the percent change for each period:
(A) From Day 1 to Day 2:
\[ \frac{12 - 20}{20} \times 100% = \frac{-8}{20} \times 100% = -0.4 \times 100% = -40% \] The magnitude is \(| -40% | = 40%\).
(B) From Day 2 to Day 3:
\[ \frac{18 - 12}{12} \times 100% = \frac{6}{12} \times 100% = 0.5 \times 100% = 50% \] The magnitude is \(| 50% | = 50%\).
(C) From Day 3 to Day 4:
\[ \frac{10 - 18}{18} \times 100% = \frac{-8}{18} \times 100% \approx -0.444 \times 100% = -44.4% \] The magnitude is \(| -44.4% | = 44.4%\).
(D) From Day 4 to Day 5:
\[ \frac{16 - 10}{10} \times 100% = \frac{6}{10} \times 100% = 0.6 \times 100% = 60% \] The magnitude is \(| 60% | = 60%\).
(E) From Day 5 to Day 6:
\[ \frac{8 - 16}{16} \times 100% = \frac{-8}{16} \times 100% = -0.5 \times 100% = -50% \] The magnitude is \(| -50% | = 50%\).
Step 4: Final Answer:
Comparing the magnitudes (40%, 50%, 44.4%, 60%, 50%), the greatest is 60%, which occurred from Day 4 to Day 5. This corresponds to option (D).