Question

4-4 & 4-5: lesson quiz 7a
the table shows the participation in a school’s debate club during the last four years.

year	1	2	3	4

between which two years did the club see the greatest growth? by what percent did it grow?
a. the greatest growth was between years 3 and 4. the growth between those years was about 32%.
b. the greatest growth was between years 1 and 2. the growth between those years was about 5%.
c. the greatest growth was between years 3 and 4. the growth between those years was about 8%.
d. the greatest growth was between years 1 and 2. the growth between those years was about 36%.

Explanation:

Step1: Calculate growth between each year pair

- Year 1 - 2: \(19 - 14 = 5\), Percent growth: \(\frac{5}{14} \approx 0.357 \approx 35.7\%\)
- Year 2 - 3: \(25 - 19 = 6\), Percent growth: \(\frac{6}{19} \approx 0.316 \approx 31.6\%\)
- Year 3 - 4: \(33 - 25 = 8\), Percent growth: \(\frac{8}{25} = 0.32 = 32\%\)

Step2: Compare growths

- Year 1 - 2: ~35.7% (Wait, no, wait: Wait, \(\frac{5}{14}\) is approx 35.7%? Wait, no, the options: Wait, option D says year 1-2, 36%. But wait, let's recalculate:

Wait, year 1-2: 14 to 19. Increase is 5. \(\frac{5}{14} \approx 0.357\) (35.7%). Year 3-4: 25 to 33, increase 8. \(\frac{8}{25} = 0.32\) (32%). Year 2-3: 6/19 ≈ 31.6%. Wait, but the options: Option A says year 3-4, 32%. Option D says year 1-2, 36%. Wait, maybe I miscalculated. Wait, 19-14=5. 5/14: 14*0.357=5, 14*0.36≈5.04. So ~36%. Then year 3-4: 8/25=0.32=32%. So between year 1-2 (36%) and year 3-4 (32%), year 1-2 has higher? But wait, the options: Let's check the options again.

Wait the options:

A. Year 3-4, 32%

B. Year 1-2, 5% (wrong, 5/14 is 35.7%)

C. Year 3-4, 8% (wrong, 8/25 is 32%)

D. Year 1-2, 36% (5/14≈35.7%≈36%)

Wait, but earlier calculation for year 1-2: 5/14≈35.7%≈36%, year 3-4: 8/25=32%. So the greatest growth is between year 1-2? But wait, the numbers: 14→19 (5), 19→25 (6), 25→33 (8). Wait, the absolute growth: 5,6,8. So absolute growth is increasing. But percentage growth: 5/14≈35.7%, 6/19≈31.6%, 8/25=32%. So percentage growth: year 1-2 (35.7%) is higher than year 3-4 (32%). So the greatest percentage growth is between year 1-2, with ~36% growth. So option D. But wait, the options: Let's check the options again.

Wait the problem: "Between which two years did the club see the greatest growth? By what percent did it grow?"

Wait, maybe I made a mistake. Wait, 14 to 19: 5. 19 to 25: 6. 25 to 33: 8. So absolute growth: 5,6,8. So absolute growth is highest between year 3-4 (8). But percentage growth: 5/14≈35.7%, 6/19≈31.6%, 8/25=32%. So percentage growth is highest between year 1-2 (35.7%≈36%). So the answer would be D? But wait, the options:

Option A: year 3-4, 32%

Option D: year 1-2, 36%

But let's check the options again. Wait, the original table:

Year 1:14, Year2:19, Year3:25, Year4:33.

Calculating percentage growth between each pair:

1-2: \(\frac{19-14}{14} \times 100 = \frac{5}{14} \times 100 \approx 35.71\% \approx 36\%\)

2-3: \(\frac{25-19}{19} \times 100 = \frac{6}{19} \times 100 \approx 31.58\% \approx 32\%\)

3-4: \(\frac{33-25}{25} \times 100 = \frac{8}{25} \times 100 = 32\%\)

So the highest percentage growth is between year 1 and 2, with ~36%, which is option D. But wait, the absolute growth is highest between year 3-4 (8), but the question is about percent growth. So the percent growth is highest between year 1-2 (36%). So the correct option is D? Wait, but let's check the options again.

Wait, the options:

A. The greatest growth was between years 3 and 4. The growth between those years was about 32%.

B. The greatest growth was between years 1 and 2. The growth between those years was about 5%.

C. The greatest growth was between years 3 and 4. The growth between those years was about 8%.

D. The greatest growth was between years 1 and 2. The growth between those years was about 36%.

So according to the calculations, the percent growth between 1-2 is ~36%, which is higher than 32% (3-4) and ~32% (2-3). So the correct answer is D.

Wait, but wait, maybe I messed up. Let's recalculate:

Year 1 to 2: (19-14)/14 *100 = 5/14 *100 ≈ 35.71% ≈ 36%

Year 3 to 4: (33-25)/25 *100 = 8/25 *100 = 32%

Year 2 to 3: (25-19)/19 *100 ≈ 31.58%

So the highest percent growth is between year 1 and 2, 36%, which is option D.

Answer:

D. The greatest growth was between years 1 and 2. The growth between those years was about 36%.