Question 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.

Open in App

Solution

Growth is dependent on three factors -initial size $(W_{0}),$ rate of growth (r) and time interval (+) for which the rate of growth is retained.

$W_{1} = W_{0} e^{r t} W_{1} = f i n a l s i z e, W_{0} = I n i t i a l s i z e, r = g r o w t h r a t e, t = t i m e, e = b a s e o f n a t u r a l l o g a r i t h m . 19 = 5 \times (2.7)^{r \times 7} \frac{19}{5} = (2.7)^{r \times 7} 3.8 = (2.7)^{r \times 7} l o g 3.8 = r \times 7 \times l o g (2.7) 0.5798 = r \times 7 \times 0.4314 \frac{0.5798}{7 \times 0.4314} = r = 0.1907 R e l a t i v e g r o w t h r a t e = \frac{G r o w t h i n g i v e n t i m e p e r i o d}{M e a s u r e m e n t a t s t a r t o f t i m e p e r i o d} = \frac{19}{5} = 3.8 c m$
Thus absolute growth rate is 0.1907 while relative growth rate is 3.8cm.

Suggest Corrections

Similar questions

A primary root grows from 5 cm to 19 cm in a week. The absolute growth rate is ________ and the relative growth rate is _______ respectively, over a period of one week.

While the population in Kolkata and Bangalore has been growing steadily towards that of the Delhi and Mumbai, the growth rate in Kolkata and Bangalore seems to be declining. Which of the following is the closest to the percent change in growth rate of 2006 (over 2005) relative to the growth rate of 2008 (over 2007) for Kolkata and Bangalore together?

Q. What is the difference between absolute growth,rate relative growth rate, geometric growth rate and Arthmetic growth rate

Q. Answer the following questions based on the information given below:

The bar chart below shows the revenue received, in million U.S.Dollars (USD), from subscribes to a particular Internet service. The data covers the period 2003 to 2007 for the United States(US) and Europe. The bar chart also shows the estimated revenues from subscription to the period 2008 to 2010.

While the subscription in Europe has been growing steadily towards that of the US, the growth rate in Europe seems to be declining. Which of the following is closest to the percent change in growth rate of 2007 (over 2006) relative to the growth rate of 2005 (over 2004)?

Join BYJU'S Learning Program

Question 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.

Question 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.