Question

Estimate the correct straight line in the log-linear scale?

(a) (If the population is growing exponentially, the curve will be concave up), (If the growth is slower than exponential, you will see a straight line), (If the growth is faster than exponential, the curve will be concave down)

(b) (If the population is growing exponentially, the curve will be concave down), (If the growth is slower than exponential, you will see a straight line), (If the growth is faster than exponential, the curve will be concave up)

(c) (If the population is growing exponentially, you will see a straight line), (If the growth is slower than exponential, the curve will be concave down), (If the growth is faster than exponential, the curve will be concave up)

(d) (If the population is growing exponentially, you will see a straight line), (If the growth is slower than exponential, the curve will be concave up), (If the growth is faster than exponential, the curve will be concave down)

This question was addressed to me in examination.

My question comes from Graph Paper with Logarithmic Coordinates topic in chapter Presentation and Analysis of Data of Bioprocess Engineering

Answer 1

The correct choice is (c) (If the population is growing exponentially, you will see a straight line), (If the growth is slower than exponential, the curve will be concave down), (If the growth is faster than exponential, the curve will be concave up)

Easy explanation: Functions plotted on the linear scale:

Figure 1:

Figure 2:

Functions plotted on the log-linear graph:

Figure 3 :

Figure 4 :

From the above graphs mentioned, Figures 2 and 4 grows exponentially while the function in Figures 1 and 3 grows slower than exponentially since the curve is concave down.