Is there a difference between logarithmic and exponential growth

Difference between logistic and exponential growth. Still have a question? Ask your own! Answering your question, graphically and taking in account the idea of bacteria growth, yes! How? Well, take a look at this graphs generated with a free app named Desmos. This is the natural log (ln) graph. As you see, imagine bacteria growing, they grow a lot and then it slows down a lot. The idea is because something is stopping massive reproduction and slows it down. Then this is the exponential graph. As you can see, reproduction starts slowly like if it’s adapting to the environment and then, boom!, reproduction is massive and with no end. What does it means? The conditions are ideal and nothing is stopping it so it grows and grows and grows indefinitely. Now, there is a graph that is the combination of the latter graphs and is known as the Logistic function graph. This function is very useful because it gives numerical answers that are acceptable and accord to real life. Why? We take in account a limit factor of growth that makes any organism grow normally until resources start to scarce and reproduction almost stops completely. This model is very accurate for predictions in Biology, Medicine, etc. So we can say any organism, living or not, first has an exponential growth and then in the point of inflection continues but with a logarithmic growth. In addition, as you can see, the graph looks like a letter “s” so this graph is named Sigmoid Graph, thanks to the greek name of the letter “s” known as Sigma. The Verhulst Formula that is used in the biological sciences is: [math]P_0[/math] = Initial population. P(t)= Population growth in any time. K= Carrying Capaity or the limit of growth. e= The Euler’s number with value 2.71828… I hope I cleared your doubts. Anything else you can ask me in comments. Have a nice day!