Search any question & find its solution
Question:
Answered & Verified by Expert
A primary root grows from $5 \mathrm{~cm}$ to $19 \mathrm{~cm}$ in a week. Calculate the growth rate and relative growth rate over the period.
Solution:
2706 Upvotes
Verified Answer
Growth depends upon three factors - initial size $\left(W_0\right)$, rate of growth $(r)$ and time interval $(+)$ for which the rate of growth is retained.
Where, $\quad W_1=W_0 e^{r t}$
$W_1=$ final size,
$W_0=$ initial size,
$r=$ growth rate,
$t=$ time
$e=$ base of natural logarithim.
$19=5 \times(2.7)^{r \times 7}$
$\frac{19}{5}=(2.7)^{r \times 7}$
$3.8=(2.7)^{r \times 7}$
$\log 38=r \times 7 \times \log (2.7)$
$0.5798=r \times 7 \times 0.4314$
$\frac{0.5798}{7 \times 0.4314}=r=0.1907$
Relative growth rate =

$=\frac{19}{5}=38 \mathrm{~cm}$
Thus absolute growth rate is $0.1907$ while relative growth rate is $3.8 \mathrm{~cm}$.
Where, $\quad W_1=W_0 e^{r t}$
$W_1=$ final size,
$W_0=$ initial size,
$r=$ growth rate,
$t=$ time
$e=$ base of natural logarithim.
$19=5 \times(2.7)^{r \times 7}$
$\frac{19}{5}=(2.7)^{r \times 7}$
$3.8=(2.7)^{r \times 7}$
$\log 38=r \times 7 \times \log (2.7)$
$0.5798=r \times 7 \times 0.4314$
$\frac{0.5798}{7 \times 0.4314}=r=0.1907$
Relative growth rate =

$=\frac{19}{5}=38 \mathrm{~cm}$
Thus absolute growth rate is $0.1907$ while relative growth rate is $3.8 \mathrm{~cm}$.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.