Ncert Exercises & Solutions

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

Growth is dependent on three factors- initial size (W₀ ), rate of growth (r) and time interval (+) for which the rate of grow this retained.

W₁ = w₀ e^rt

Where,

W₁ = Final size,

W₀ = Initial size,

r = growth rate

t = time

e = base of natural logarithm

19 = 5 x (2.7)^{r x 7}

\frac{19}{5}

= (2.7)^{r x 7}

3.8 = 5 x (2.7)^{r x 7}

log 3.8 = r x 7 x log(2.7)

0.5798 = r x 7 x 0.4314

\frac{0.5798}{7 \times 0.4314}

= r = 0.1907

Relative growth rate =

\frac{Growth in given time period}{Measurement at start of time period}

\frac{19}{5}

= 3.8 cm