Download presentation

Presentation is loading. Please wait.

Published byMacey Sandoval Modified over 4 years ago

1
Whether does the number e come from!?!?

2
Suppose the number of bacteria, n 0, in a dish doubles in unit time. If a very simple growth model is adopted, you can think of the number of bacteria remaining constant during the period and then, at t = 1, the number doubles instantaneously. … but this is not very realistic

3
To make it more realistic, suppose that the number of bacteria remains constant during the periods 0≤t<0.1, 0.1 ≤t<0.2, 0.2 ≤t<0.3, …, 0.9 ≤t<1 and the number of bacteria grows by 10% (one tenth) at times t=0.1, t=0.2, t=0.3, …, t=0.9, t=1

4
Then, when t=1, the number of bacteria is *Note that the number has more than doubled. In fact, it has increased by a factor of almost 2.6 because of the compounding effect.

5
Ultimately, the smaller the length of the time interval, the more accurate the growth model is. For example, if the number of bacteria remains constant during the periods 0≤t<0.01, 0.01 ≤t<0.02, 0.02 ≤t<0.03, …, 0.99 ≤t<1 and the number of bacteria grows by 1% (one hundredth) at times t=0.01, t=0.02, t=0.03, …, t=0.99, t=1

6
Then what is the formula for the number of bacteria?

Similar presentations

OK

Exponential and Logarithmic Functions 4 Copyright © Cengage Learning. All rights reserved.

Exponential and Logarithmic Functions 4 Copyright © Cengage Learning. All rights reserved.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google