Question

The following data were obtained from an experiment on a tissue culture showing exponential growth:
Initial weight (in grams) Final weight (in grams) Time of growth (in seconds)

2	4	1

What is the relative growth rate in g/s?

• A. 0.693
• B. 2.100
• C. 3.523
• D. 4.612

Answer 1

The correct option is A 0.693

Given data:
Initial weight of the plant tissue culture, $W_0$ = 2 g
Final weight of the plant tissue culture, $W_1$ = 4 g
Time of growth, t = 1 s

Calculation: For exponential growth, $W_1$ = $W_0$$e^r$${}^t$ - equation (i)
where $W_1$ is the final size (weight, number, height, etc.) of a sample (for example, cell culture),
$W_0$ is the initial size (weight, number, height, etc.) of a sample,
r is the relative growth rate,
t is the time of growth and e is the base of natural logarithms.

Replacing $W_1$,$W_0$ with their given values in equation (i)
4 = 2$e^r$
2 = $e^r$
Taking log on both sides,
$lo{g}_e$(2) = $lo{g}_e$$e^r$
Since, [$lo{g}_e$$e^r$]=r
r = $lo{g}_e$(2)=0.693
Therefore, the relative growth rate is 0.693 g/s.