For the Growth option, if the step value is 1.05, each successive value will be what percent above the previous value?

Question

BlackTom AI · Accepted Answer

A step value of 1.05 is a multiplicative growth factor, so each successive value is 1.05 times the previous value.

1) Relevant knowledge points and concepts
- A growth "step value" like 1.05 is a multiplier. Multipliers greater than 1 indicate percentage increases.
- Percent increase from multiplier m is (m − 1) × 100%.
- Interpreting multipliers correctly avoids confusing absolute values (e.g., 1.05) with percentage changes (e.g., 5%).

2) Complete reasoning process, step by step
- Start with the multiplier m = 1.05.
- Find the change relative to the previous value by subtracting 1 (the original 100%): change = m − 1.
- Convert that change to a percent by multiplying by 100%.

3) Calculations with all intermediate steps
- m − 1 = 1.05 − 1 = 0.05
- Percent increase = 0.05 × 100% = 5%

Example numeric check:
- If the previous value is 100, new value = 100 × 1.05 = 105.
- Absolute increase = 105 − 100 = 5, which is 5/100 = 0.05 = 5%.

4) Why the correct answer is correct
- The multiplier 1.05 means the new amount equals the old amount plus 5% of the old amount. Subtracting 1 isolates the fractional increase (0.05), and converting to percent yields 5%.

5) Why other common interpretations are incorrect
- Interpreting 1.05 as 105% is a representation of the new total (100% + 5%), not the percent above the previous value. Saying “105%” describes the new value relative to the original, but the question asks how much percent above the previous value, which is 5%.
- Saying 0.05% or 1.05% confuses the fractional increase with percentage points and is incorrect; the correct conversion is 0.05 → 5%.

6) Conclusion
The percent each successive value is above the previous value is 5%, which matches the provided answer.

For the Growth option, if the step value is 1.05, each successive value will be what percent above the previous value?Single choice

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