How Can We Use Calculus to Predict Population Growth?

In summary, the conversation revolves around determining the correct formula for population growth over time, with an initial equation of dP/dt = 0.2P. After some discussion and clarifications, it is concluded that the correct formula is dP/P = 0.2dt, which can be integrated to find the population in t years.
  • #1
Sirsh
267
10
Hi all, I'm just wondering if this is correct: [tex]\frac{dP}{dt}[/tex] =0.2P If the population is now 5300:
(a) Write a formula for the population in t years time.

To do this would i antidifferntiate 0.2P, so.. (0.2P^2)/2 = 0.1P^2 + t?

Thank you!
 
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  • #2
No that is wrong. dP and 0.2P are on opposite sides. Rewrite the equation in such a way that all Ps are on the same side and all ts on the other side.
 
  • #3
dP/0.2P = dt? or dP/P = 0.2dt
 
  • #4
Both are correct. Now you can integrate both sides of that equation.
 
  • #5
Um, Does the equation mean that: the derivative of P divided by P equals 0.2 times the derivative of t?
 
  • #6
No [itex]dP=\frac{dP}{dt} dt[/itex], but as you can see they are very closely related. Just put the integral sign in front of both sides of the equation and it will become clear what to do.
 

FAQ: How Can We Use Calculus to Predict Population Growth?

What is calculus and how is it used in science?

Calculus is a branch of mathematics that studies the properties of continuous change. It is used in science to model and analyze a wide range of natural phenomena, from motion and forces to growth and decay of populations.

What are some common applications of calculus?

Some common applications of calculus include optimization problems, finding maximum and minimum values, and calculating rates of change. It is also used in fields such as physics, engineering, economics, and biology to model real-world systems and make predictions.

How does calculus help in understanding motion and forces?

Calculus is essential in understanding motion and forces as it allows us to describe and analyze the behavior of moving objects. By using calculus, we can calculate velocity, acceleration, and other important quantities that help us understand how objects move and interact with each other.

How is calculus used in economics and finance?

Calculus is widely used in economics and finance to study and predict changes in supply and demand, consumer behavior, and market trends. It is also used in financial analysis to calculate interest rates, compound interest, and investment returns.

What are some practical applications of calculus in everyday life?

Some practical applications of calculus in everyday life include designing structures such as bridges and buildings, predicting weather patterns, and optimizing transportation routes. It is also used in medicine to model and understand biological processes and in computer science to develop algorithms and data analysis techniques.

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