Answer :
Answer: 9 days
Explanation:
- Step 1
Let the rate of Leaf growth r be defined as, [tex]\frac{Increase in area}{time taken}[/tex] = [tex]\frac{A1 - A}{t}[/tex]
where A is initial area of the leaf, A1 is the final area of the leaf and t is the time taken for the increase in Area.
- Express the proportional relationship in equation.
Given that rate of leaf growth, r is proportional to the surface area of the leaf A. we have r ∝ A.
r = kA, where k is the rate constant.
therefore, k = [tex]\frac{r}{A}[/tex]
when A = 2[tex]cm^{2}[/tex], A1 = 3
so k = [tex]\frac{\frac{3 - 2}{3}}{2}[/tex]
= [tex]\frac{1}{3}[/tex] ÷ 2
= 0.33 ÷ 2
k = 0.167
- After calculating the rate constant k, we then find the time t when A1 is 5[tex]cm^{2}[/tex]
- we have r = k × A1 = [tex]\frac{A1 - A}{t}[/tex]
so, 0.167 × 2 = [tex]\frac{5 - 2}{t}[/tex]
0.33 = [tex]\frac{3}{t}[/tex].
t = 3/0.33
Therefore, t = 9 days.