# Carbon dating using exponential growth

From population growth and continuously compounded interest to radioactive decay and Newton’s law of cooling, exponential functions are ubiquitous in nature.In this section, we examine exponential growth and decay in the context of some of these applications. These systems follow a model of the form Population growth is a common example of exponential growth. It seems plausible that the rate of population growth would be proportional to the size of the population.

After all, the more bacteria there are to reproduce, the faster the population grows.

[link] and [link] represent the growth of a population of bacteria with an initial population of Note that we are using a continuous function to model what is inherently discrete behavior.

One of the most prevalent applications of exponential functions involves growth and decay models.

Exponential growth and decay show up in a host of natural applications.

And that's useful, but what if I care about how much carbon I have after 1/2 a year, or after 1/2 a half life, or after three billion years, or after 10 minutes? A general function, as a function of time, that tells me the number, or the amount, of my decaying substance I have.

So that's what we're going to do in this video..pass_color_to_child_links a.u-inline.u-margin-left--xs.u-margin-right--sm.u-padding-left--xs.u-padding-right--xs.u-relative.u-absolute.u-absolute--center.u-width--100.u-flex-inline.u-flex-align-self--center.u-flex-justify--between.u-serif-font-main--regular.js-wf-loaded .u-serif-font-main--regular.amp-page .u-serif-font-main--regular.u-border-radius--ellipse.u-hover-bg--black-transparent.web_page .u-hover-bg--black-transparent:hover. Content Header .feed_item_answer_user.js-wf-loaded . And just to maybe make that a little bit more intuitive, imagine a situation here where you have 1 times 10 to the 9th. And let's say over here you have 1 times 10 to the 6th carbon atoms.And if you look at it at over some small period of time, let's say, if you look at it over one second, let's say our dt.Exponential functions can also be used to model populations that shrink (from disease, for example), or chemical compounds that break down over time.

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