During exponential (log) growth, how is the growth rate commonly expressed and related to generation time?

Introduction / Context:
Quantifying how fast a population grows requires clear terminology. In the exponential phase, growth is characterized by constant proportional increase, enabling precise mathematical relationships between growth rate and generation time.

Given Data / Assumptions:

• Growth is balanced and specific growth rate is constant.
• One generation equals one doubling.
• Time is measured over an interval where exponential behavior holds.

Concept / Approach:
If a culture undergoes n doublings per unit time, the growth rate in generations per unit time is simply n. Generation time, g, is the time per doubling, so growth rate = 1 / g. These are two equivalent ways of expressing the same phenomenon. In parallel, the specific growth rate mu relates as mu = ln(2) / g.

Step-by-Step Solution:
Define generation time g as time per doubling. Express growth rate as doublings per time = 1 / g. Recognize that “generations per unit time” and “reciprocal of g” are equivalent. Select the option combining both statements.

Verification / Alternative check:
A culture with g = 20 minutes produces 3 generations per hour; conversely, 3 generations per hour implies g = 60/3 = 20 minutes.

Why Other Options Are Wrong:
Each partial statement is correct but incomplete by itself; “none” is clearly false.

Common Pitfalls:
Mixing up specific growth rate (per hour) with generations per hour; remember mu = ln(2) * generations per hour.

Final Answer:
both (a) and (b).