Answer:
The rate of growth of sprout seed in 3 months is 1.14%
Step-by-step explanation:
Given as :
The length of seed sprout grew = [tex]\dfrac{2}{3}[/tex] foot
The time period for sprout grew = 3 month
Let The rate of sprout grew = r%
Let The initial length of seed = l foot
So, The length of seed sprout grew after 3 months = [tex]\dfrac{2}{3}[/tex] × l foot
Now, According to question
The length of seed sprout grew after n months = [tex]\dfrac{\textrm initial length}{(1+\frac{rate}{100})^{\textrm time}}[/tex]
Or , [tex]\dfrac{2}{3}[/tex] × l = [tex]\dfrac{\textrm l}{(1+\frac{rate}{100})^{\textrm time}}[/tex]
Or, [tex](1+\dfrac{r}{100})^{3}[/tex] = [tex]\dfrac{3}{2}[/tex]
Or, 1 + [tex]\dfrac{r}{100}[/tex] = [tex](1.5)^{\frac{1}{3}}[/tex]
Or, [tex]\dfrac{r}{100}[/tex] = 1.14
∴ r = 1.14 ×100 = 114
So, The rate of growth = r = 1.14 %
Hence The rate of growth of sprout seed in 3 months is 1.14% Answer
