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  • A primary root grows from 5 cm to 19 cm in a week. Calculate the growth rate and relative growth rate over the period.

A primary root grows from 5 cm to 19 cm in a week. Calculate the growth rate and relative growth rate over the period.

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Ans.

Absolute Growth rate can be calculated as follows:
W_1 = W_0 e^{rt}
Where W1 = final Size (weight, height, number etc.)
W0 = initial Size at the beginning of the period
r = growth rate
t= time of growth
e = base of natural logarithms
Here, r is the relative growth rate
Given W1 = 19 cm
W0 = 5 cm
t =7 days
or,
Using W1 = W0 ert
We \: \: get\: \: 19 = 5 \times (2.7)^{7× r}

Then
Then 3.8 = (2.7) ^{7× r}
Then taking log on both the sides,
\log 3.8 = 7r \times \log 2.7
Then, 0.5798 = 7r \times 0.4314
 

r=\frac{0.5798}{7\times 0.4314}
Or r = 0.1907
Relative growth rate can be calculated as follows:

r=\frac{final \: size}{initial \: size}

r=\frac{19}{5}
r = 3.8 cm
Absolute growth rate= 0.1907
Relative growth rate 3.8 cm

 

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