Question

using the instructions you made, construct a line graph using the data below and answer the following questions independently. call your teacher over to check your work when you are done. table 1 effect of fertilizer on plant growth fertilizer concentration (%) plant growth (mm) 1 2 3 4 5 6 7 8 9 5 1. how much growth would you predict at 4 percent fertilizer concentration? 2. if you wanted a plant to grow at the maximum rate, what percent fertilizer concentration would you recommend? why? 3. what do you think might happen if you used a concentration 15 percent? 4. which do you find easier to read, the table or the graph? why?

Explanation:

Step1: Assume linear relationship for prediction

Since the data shows a somewhat linear - like trend (1, 2), (3, 4), (5, 6), (7, 8), we can assume a linear relationship between fertilizer concentration (x) and plant growth (y). The general form of a linear equation is $y=mx + b$. Using two points (1, 2) and (3, 4), we first find the slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4 - 2}{3 - 1}=1$. Then substituting $x = 1,y = 2$ into $y=mx + b$, we get $2=1\times1 + b$, so $b = 1$. The equation is $y=x + 1$.

Step2: Predict growth at 4%

Substitute $x = 4$ into $y=x + 1$. Then $y=4 + 1=5$.

Step3: Analyze maximum growth

From the given data (1, 2), (3, 4), (5, 6), (7, 8), (9, 5), the highest growth value is 8 which occurs at 7 percent fertilizer concentration. So 7 percent is recommended as it has the highest observed growth so far.

Step4: Predict at 15%

Since the growth starts to decrease from 9 percent (from 8 at 7 percent to 5 at 9 percent), it is likely that at 15 percent, the growth will be lower than 5, possibly due to over - fertilization which can cause problems like root burn and nutrient imbalances.

Step5: Compare table and graph

Graph is usually easier to read as it provides a visual representation of the relationship between fertilizer concentration and plant growth. It is easier to identify trends, such as increase or decrease, and make predictions visually compared to looking at individual data points in a table.

Answer:

1. 5 mm
2. 7 percent; because it has the highest observed plant growth in the given data.
3. The plant growth is likely to be lower than 5 mm, possibly due to over - fertilization issues.
4. The graph; because it provides a visual representation making it easier to identify trends and make predictions.