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A population of protozoa develops with a constant relative growth of 0.7944 per member per day. On day zero the population consists of 2 members. Find the population size after six days.
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02:23
Yiming Zhang
00:27
Amrita Bhasin
00:50
Heather Zimmers
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 8
Exponential Growth and Decay
Derivatives
Differentiation
Oregon State University
Harvey Mudd College
University of Michigan - Ann Arbor
Idaho State University
Lectures
04:40
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
44:57
In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.
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Alright, here's a fun problem. We have protozoa population. Protozoa and it grows Um by 79.44% of its members. Um that are currently there. So the rate of change of P. With time where PSR members of our protozoa population Is then I can write as .7944 p. Um At the start we have two members and R. T. Is in day. So our goal is to find um the number of protozoa members on day six. So basically after six days. So when she or I'll just rewrite it At T. equals six days. Okay well when we have this is exponential growth. So our general form is PFT Equals p. at zero E. To the Katie. Now notice oops I wrote it here all e to the Katie. Uh this is our case. So we actually have values and this we already have P. A zero. So we have quite a bit, we can plug in so we can plug in R. Two and then E. To the 20.7944 T. So that's our general equation. But we want Um to find out our number of members when T. is six days. So we are going to go ahead and need our calculator here because we have to put all that in our calculator. And when we do that, our value is 234.99 members. But we want to round up to the nearest members. So we'll go ahead and make that approximately 230 Five members of Protozoa family after six days. Very nice, grows pretty fast. Okay. I hope that helped to have a fantastic rest of your day.
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