What is the best deal for maximum profit?

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In summary, the given model is used to find the growth of an endangered species population. The limit of P(t) as t approaches positive infinity is 500, according to the textbook. It is possible to graph this model, but it may not be the best approach to finding the limit. The points on the graph of P(t) are in the form (t, P(t)). The problem is asking for the limit of P(t) as t approaches infinity, and using the properties of exponential functions, we can determine that the limit is 500.
  • #1
nycmathdad
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The model below is given to find the growth of a population of an endangered species.

P(t) = (500)/[1 + 82.3e^(-0.162t)]

Find the limit of P(t) as t tends to positive infinity.

The answer in the textbook is 500.

Can a model like this be graphed? If so, is the graph of P(t) the best approach to find the limit?
Points on the graph of P(t) are in the form (t, P(t)). Correct?
 
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  • #2
Beer soaked ramblings follow.
nycmathdad said:
The model below is given to find the growth of a population of an endangered species.

P(t) = (500)/[1 + 82.3e^(-0.162t)]

Find the limit of P(t) as t tends to positive infinity.

The answer in the textbook is 500.

Can a model like this be graphed? If so, is the graph of P(t) the best approach to find the limit?
Points on the graph of P(t) are in the form (t, P(t)). Correct?
Problem 1.5.79.a.
Again, you left out a lot of details.
A screenshot will be helpful.
The problem is asking you to find $\lim_{t \to \infty} P(t)$
 
  • #3
I am interested in 79 partn(a) only.

Here it is:

Screenshot_20210402-185104_Drive.jpg
 
  • #4
nycmathdad said:
The model below is given to find the growth of a population of an endangered species.

P(t) = (500)/[1 + 82.3e^(-0.162t)]

Find the limit of P(t) as t tends to positive infinity.

The answer in the textbook is 500.

Can a model like this be graphed? If so, is the graph of P(t) the best approach to find the limit?
Points on the graph of P(t) are in the form (t, P(t)). Correct?

It's an exponentially decaying function due to the negative power on e. So what value do you think that the exponential function tends to?
 
  • #5
Prove It said:
It's an exponentially decaying function due to the negative power on e. So what value do you think that the exponential function tends to?

Well, 82.3e^(-0.162t)] becomes zero leaving the expressing 500/1. The limit is 500.
 
  • #6
nycmathdad said:
Well, 82.3e^(-0.162t)] becomes zero leaving the expressing 500/1. The limit is 500.

Correct.
 
  • #7
Prove It said:
Correct.

Me correct? Really? Wow!
 
  • #8
Beer soaked non sequitur ramblings follow.
nycmathdad said:
Me ...
The best deal is the one that brings the most profit.
 

FAQ: What is the best deal for maximum profit?

What is the best deal for maximum profit?

The best deal for maximum profit depends on several factors, including the industry, market conditions, and the company's goals. It is not a one-size-fits-all answer and requires careful analysis and research.

How can I determine the best deal for maximum profit?

To determine the best deal for maximum profit, you need to consider the cost of production, market demand, competition, and potential risks. Conducting a thorough cost-benefit analysis and market research can help you make an informed decision.

What are some common strategies for maximizing profit?

Some common strategies for maximizing profit include cost-cutting, increasing sales, diversifying products or services, and expanding into new markets. It is essential to find a balance between these strategies and consider the potential risks and benefits of each.

How do I know if a deal will bring maximum profit?

There is no guarantee that a deal will bring maximum profit, as it depends on various factors. However, you can evaluate the deal's potential by analyzing the market demand, competition, and projected costs and revenues. It is also crucial to consider any potential risks or challenges that may arise.

What are some potential risks to consider when looking for the best deal for maximum profit?

Some potential risks to consider when looking for the best deal for maximum profit include changes in market conditions, competition, supply chain disruptions, and unexpected expenses. It is essential to conduct a risk analysis and have contingency plans in place to mitigate these risks.

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