Questions on plant growth and optimization of growing conditions.
The optimal growth can be determined by comparing plant height per unit acid added. For example, for 20 ml acid added, plant grew by 18.5 cm; that is, plant grew at 0.925 cm/ml of acid. Similar number for other acid additions are:
20 ml 0.925 cm/ml
30 ml 0.69 cm/ml
40 ml 1.13 cm/ml
50 ml 1.246 cm/ml
60 ml 0.177 cm/ml
Thus, 50 ml is the most optimal acid addition.
Interpolation can help us determine the approximate plant growth at 35 ml acid addition.
Plant grew 20.7 cm and 45.2 cm for 30 ml and 40 ml acid addition. That is, for each ml acid addition, plant grew by 2.45 cm (= (45.2-20.7)/10). Thus, for 35 ml acid addition, plant will grow to approximately, 32.95 cm (= 20.7 + 5 x 2.45), or approximately 33 cm.
If the plant height is 59 cm, then the acid addition is between 40 and 50 ml (from the table). One way to solve it is by interpolation. Between 40 ml and 50 ml acid addition, each ml acid addition caused 1.71 cm (= (62.3-45.2)/10) of plant growth.
Thus, 59 = 45.2 + Vx1.71
solving this we get, V = 8.07 ml
that is, the amount of acid added was, 40 + 8.07 = 48.07 ml or about 48 ml.
Thus, (about) 48 ml of acid caused 59 cm of plant growth.
Hope this helps.