Question

Which one of the following plots represents exponential growth? 

 

• A. A
• B. B
• C. C
• D. D

Hint:

To recognize exponential growth, check for a linear relationship between \( \ln N \) and time \( t \).

Answer 1

The Correct Option is B

Step 1: Understanding Exponential Growth.
Exponential growth occurs when the rate of growth is proportional to the current size. In mathematical terms, \( N(t) = N_0 e^{kt} \), where \( N \) is the population size, \( t \) is time, and \( k \) is the growth constant. The relationship between \( N \) and \( t \) is exponential.
Step 2: Analyzing the Graphs.
- (A) N vs t: This would show a curve that increases rapidly, which is characteristic of exponential growth, but not in a linear manner.
- (B) ln N vs t: Taking the natural logarithm of \( N \) linearizes the exponential growth curve. This would produce a straight line, indicating exponential growth.
- (C) N vs ln t: This would show a non-linear relationship, not exponential growth.
- (D) ln N vs ln t: This would correspond to a power-law relationship, not exponential growth.
Step 3: Conclusion.
Thus, the correct plot representing exponential growth is (B) ln N vs t.