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My name is Ann [436]

4 years ago

13

How quickly a leaf grows is proportional how big [ie the surface area] the leaf is. If the area of the leaf grows from 2cm2 to 3

cm2 in 3 days, how long will it take for the leaf's area to increase to 5 cm2

1 answer:

marusya05 [52]4 years ago

3 0

Answer: 9 days

Explanation:

Step 1

Let the rate of Leaf growth <em>r</em> be defined as, $\frac{Increase in area}{time taken}$ = $\frac{A1 - A}{t}$

where <em>A</em> is initial area of the leaf, <em>A1</em> is the final area of the leaf and<em> t</em> 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 = $\frac{r}{A}$

when A = 2 $cm^{2}$ , A1 = 3

so k = $\frac{\frac{3 - 2}{3}}{2}$

= $\frac{1}{3}$ ÷ 2

= 0.33 ÷ 2

k = 0.167

After calculating the rate constant k, we then find the time t when A1 is 5 $cm^{2}$

we have r = k × A1 = $\frac{A1 - A}{t}$

so, 0.167 × 2 = $\frac{5 - 2}{t}$

0.33 = $\frac{3}{t}$ .

t = 3/0.33

Therefore, t = 9 days.

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