For bacterial growth in a cell culture, growth law is very similar to the law of radioactive decay. Which of the following graphs is most suitable to represent bacterial colony growth ?
Where N - Number of Bacteria at any time, N₀ - Initial number of Bacteria.

Solution

Chemistry ma’am · 3 steps

Same first-order law as radioactive decay, but with a plus sign: the colony grows exponentially from 1.

1. Write the rate law. In radioactive decay the rate is proportional to the number present, so it is first order. Bacteria multiply the same way: the more bacteria there are, the faster new ones form. The only change is that N goes up instead of down, so dN/dt = +kN.

   N/N₀ = eᵏᵗ

2. Read the shape. At t = 0 the ratio is e⁰ = 1, so the curve starts above the origin. After that it rises ever more steeply, because the slope kN grows as N grows.

   Option	Shape of the graph	Fits N/N₀ = eᵏᵗ?
   (a)	Falls along a curve from a high value	No, this is first-order decay
   (b)	Falls along a straight line	No, this is zero-order loss
   (c)	Starts at a nonzero value, rises more and more steeply	Yes
   (d)	Starts at zero, rises, then levels off	No, wrong start and it slows down

3. So. Only graph (c) shows exponential growth that starts at N/N₀ = 1 and keeps speeding up. The answer is (c).

The idea to keep. Similar to radioactive decay means first order, so the graph is an exponential. Then check the sign: growth curves upwards from N/N₀ = 1, while decay falls from it.

Answer from the NTA final answer key. Solution by PrepWiser.