What does the term 'rate' mean in maths [duplicate]

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This question already has an answer here:

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  What does rate of change actually mean?
  
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For example birth rate, death rate in population modelling. Correct me if I'm wrong, but does this mean a certain number of births or deaths over a period of time?

Aslo, rate of change in calculus when dealing with derivatives. Does this mean infinitesimal change with respect to another quantity. How much y changes when we change x quantity. Can someone please give me some laymen term examples to confidently understand this.

I've looked elsewhere online for clarification, but nothing seems to be resolving my Confusion.

calculus soft-question

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asked Jan 19 at 23:03

user606466

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marked as duplicate by Key Flex, Shailesh, user91500, Lee David Chung Lin, Pacciu Jan 20 at 11:09

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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0

$begingroup$

This question already has an answer here:

• 
  What does rate of change actually mean?
  
  3 answers
  
  

For example birth rate, death rate in population modelling. Correct me if I'm wrong, but does this mean a certain number of births or deaths over a period of time?

Aslo, rate of change in calculus when dealing with derivatives. Does this mean infinitesimal change with respect to another quantity. How much y changes when we change x quantity. Can someone please give me some laymen term examples to confidently understand this.

I've looked elsewhere online for clarification, but nothing seems to be resolving my Confusion.

calculus soft-question

share|cite|improve this question

asked Jan 19 at 23:03

user606466

$endgroup$

marked as duplicate by Key Flex, Shailesh, user91500, Lee David Chung Lin, Pacciu Jan 20 at 11:09

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

add a comment | 

0

0

0

$begingroup$

This question already has an answer here:

• 
  What does rate of change actually mean?
  
  3 answers
  
  

For example birth rate, death rate in population modelling. Correct me if I'm wrong, but does this mean a certain number of births or deaths over a period of time?

Aslo, rate of change in calculus when dealing with derivatives. Does this mean infinitesimal change with respect to another quantity. How much y changes when we change x quantity. Can someone please give me some laymen term examples to confidently understand this.

I've looked elsewhere online for clarification, but nothing seems to be resolving my Confusion.

calculus soft-question

share|cite|improve this question

asked Jan 19 at 23:03

user606466

$endgroup$

This question already has an answer here:

• 
  What does rate of change actually mean?
  
  3 answers
  
  

For example birth rate, death rate in population modelling. Correct me if I'm wrong, but does this mean a certain number of births or deaths over a period of time?

Aslo, rate of change in calculus when dealing with derivatives. Does this mean infinitesimal change with respect to another quantity. How much y changes when we change x quantity. Can someone please give me some laymen term examples to confidently understand this.

I've looked elsewhere online for clarification, but nothing seems to be resolving my Confusion.

This question already has an answer here:

• 
  What does rate of change actually mean?
  
  3 answers
  
  

calculus soft-question

calculus soft-question

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asked Jan 19 at 23:03

user606466

share|cite|improve this question

asked Jan 19 at 23:03

user606466

share|cite|improve this question

share|cite|improve this question

asked Jan 19 at 23:03

user606466

asked Jan 19 at 23:03

user606466

asked Jan 19 at 23:03

user606466

marked as duplicate by Key Flex, Shailesh, user91500, Lee David Chung Lin, Pacciu Jan 20 at 11:09

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

marked as duplicate by Key Flex, Shailesh, user91500, Lee David Chung Lin, Pacciu Jan 20 at 11:09

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

add a comment | 

add a comment | 

3 Answers
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Rate implies it's a relative measure, typically a ratio, compared to some other quantity. For example death rate could be per unit of time or could be per hundred thousand people or per war. A rate of change is a special case where a function changes with respect to a variable and we compare the relative rates of change between the input and the output.

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answered Jan 19 at 23:09

CyclotomicFieldCyclotomicField

2,4431314

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Rate = Speed

If your birth function varied continuously the rate at which it varied would be the derivative of the function.

For discrete functions the rate is usually synonymous to the difference or the difference of consecutive terms divided by time units.

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answered Jan 19 at 23:09

Sorin TircSorin Tirc

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You're right; birth and death rates are measures of how often, people perhaps, are born and die. What's important, though, is what this measure is with respect to. It's valid to say about 4 people are born per second, but it's also valid to say about 2 people are born per death.

What's interesting is that the statistic that we're told is an average of the actual birth/death rate. Maybe as you're reading this, the death rate is 1.7 people per second, and perhaps now it's 1.9 people per second. So it averages, more or less, to almost 2 people per second.

The derivative gives information about how fast something is changing and in what direction. What's neat is Earth's population is huge, ~7.6 billion people, but both the birth and death rates are very small in comparison, about 4 and 2 people per second respectively. So we can use that to predict that Earth's population is overall increasing (direction) at a rate of ~2 people per second (speed).

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answered Jan 19 at 23:32

AEngineerAEngineer

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3 Answers
3

active

oldest

votes

3 Answers
3

active

oldest

votes

active

oldest

votes

active

oldest

votes

1

$begingroup$

Rate implies it's a relative measure, typically a ratio, compared to some other quantity. For example death rate could be per unit of time or could be per hundred thousand people or per war. A rate of change is a special case where a function changes with respect to a variable and we compare the relative rates of change between the input and the output.

share|cite|improve this answer

answered Jan 19 at 23:09

CyclotomicFieldCyclotomicField

2,4431314

$endgroup$

add a comment | 

1

$begingroup$

Rate implies it's a relative measure, typically a ratio, compared to some other quantity. For example death rate could be per unit of time or could be per hundred thousand people or per war. A rate of change is a special case where a function changes with respect to a variable and we compare the relative rates of change between the input and the output.

share|cite|improve this answer

answered Jan 19 at 23:09

CyclotomicFieldCyclotomicField

2,4431314

$endgroup$

add a comment | 

1

1

1

$begingroup$

Rate implies it's a relative measure, typically a ratio, compared to some other quantity. For example death rate could be per unit of time or could be per hundred thousand people or per war. A rate of change is a special case where a function changes with respect to a variable and we compare the relative rates of change between the input and the output.

share|cite|improve this answer

answered Jan 19 at 23:09

CyclotomicFieldCyclotomicField

2,4431314

$endgroup$

Rate implies it's a relative measure, typically a ratio, compared to some other quantity. For example death rate could be per unit of time or could be per hundred thousand people or per war. A rate of change is a special case where a function changes with respect to a variable and we compare the relative rates of change between the input and the output.

share|cite|improve this answer

answered Jan 19 at 23:09

CyclotomicFieldCyclotomicField

2,4431314

share|cite|improve this answer

share|cite|improve this answer

answered Jan 19 at 23:09

CyclotomicFieldCyclotomicField

2,4431314

answered Jan 19 at 23:09

CyclotomicFieldCyclotomicField

2,4431314

answered Jan 19 at 23:09

CyclotomicFieldCyclotomicField

2,4431314

2,4431314

add a comment | 

add a comment | 

0

$begingroup$

Rate = Speed

If your birth function varied continuously the rate at which it varied would be the derivative of the function.

For discrete functions the rate is usually synonymous to the difference or the difference of consecutive terms divided by time units.

share|cite|improve this answer

answered Jan 19 at 23:09

Sorin TircSorin Tirc

1,785213

$endgroup$

add a comment | 

0

$begingroup$

Rate = Speed

If your birth function varied continuously the rate at which it varied would be the derivative of the function.

For discrete functions the rate is usually synonymous to the difference or the difference of consecutive terms divided by time units.

share|cite|improve this answer

answered Jan 19 at 23:09

Sorin TircSorin Tirc

1,785213

$endgroup$

add a comment | 

0

0

0

$begingroup$

Rate = Speed

If your birth function varied continuously the rate at which it varied would be the derivative of the function.

For discrete functions the rate is usually synonymous to the difference or the difference of consecutive terms divided by time units.

share|cite|improve this answer

answered Jan 19 at 23:09

Sorin TircSorin Tirc

1,785213

$endgroup$

Rate = Speed

If your birth function varied continuously the rate at which it varied would be the derivative of the function.

For discrete functions the rate is usually synonymous to the difference or the difference of consecutive terms divided by time units.

share|cite|improve this answer

answered Jan 19 at 23:09

Sorin TircSorin Tirc

1,785213

share|cite|improve this answer

share|cite|improve this answer

answered Jan 19 at 23:09

Sorin TircSorin Tirc

1,785213

answered Jan 19 at 23:09

Sorin TircSorin Tirc

1,785213

answered Jan 19 at 23:09

Sorin TircSorin Tirc

1,785213

1,785213

add a comment | 

add a comment | 

0

$begingroup$

You're right; birth and death rates are measures of how often, people perhaps, are born and die. What's important, though, is what this measure is with respect to. It's valid to say about 4 people are born per second, but it's also valid to say about 2 people are born per death.

What's interesting is that the statistic that we're told is an average of the actual birth/death rate. Maybe as you're reading this, the death rate is 1.7 people per second, and perhaps now it's 1.9 people per second. So it averages, more or less, to almost 2 people per second.

The derivative gives information about how fast something is changing and in what direction. What's neat is Earth's population is huge, ~7.6 billion people, but both the birth and death rates are very small in comparison, about 4 and 2 people per second respectively. So we can use that to predict that Earth's population is overall increasing (direction) at a rate of ~2 people per second (speed).

share|cite|improve this answer

answered Jan 19 at 23:32

AEngineerAEngineer

1,5441317

$endgroup$

add a comment | 

0

$begingroup$

You're right; birth and death rates are measures of how often, people perhaps, are born and die. What's important, though, is what this measure is with respect to. It's valid to say about 4 people are born per second, but it's also valid to say about 2 people are born per death.

What's interesting is that the statistic that we're told is an average of the actual birth/death rate. Maybe as you're reading this, the death rate is 1.7 people per second, and perhaps now it's 1.9 people per second. So it averages, more or less, to almost 2 people per second.

The derivative gives information about how fast something is changing and in what direction. What's neat is Earth's population is huge, ~7.6 billion people, but both the birth and death rates are very small in comparison, about 4 and 2 people per second respectively. So we can use that to predict that Earth's population is overall increasing (direction) at a rate of ~2 people per second (speed).

share|cite|improve this answer

answered Jan 19 at 23:32

AEngineerAEngineer

1,5441317

$endgroup$

add a comment | 

0

0

0

$begingroup$

You're right; birth and death rates are measures of how often, people perhaps, are born and die. What's important, though, is what this measure is with respect to. It's valid to say about 4 people are born per second, but it's also valid to say about 2 people are born per death.

What's interesting is that the statistic that we're told is an average of the actual birth/death rate. Maybe as you're reading this, the death rate is 1.7 people per second, and perhaps now it's 1.9 people per second. So it averages, more or less, to almost 2 people per second.

The derivative gives information about how fast something is changing and in what direction. What's neat is Earth's population is huge, ~7.6 billion people, but both the birth and death rates are very small in comparison, about 4 and 2 people per second respectively. So we can use that to predict that Earth's population is overall increasing (direction) at a rate of ~2 people per second (speed).

share|cite|improve this answer

answered Jan 19 at 23:32

AEngineerAEngineer

1,5441317

$endgroup$

You're right; birth and death rates are measures of how often, people perhaps, are born and die. What's important, though, is what this measure is with respect to. It's valid to say about 4 people are born per second, but it's also valid to say about 2 people are born per death.

What's interesting is that the statistic that we're told is an average of the actual birth/death rate. Maybe as you're reading this, the death rate is 1.7 people per second, and perhaps now it's 1.9 people per second. So it averages, more or less, to almost 2 people per second.

The derivative gives information about how fast something is changing and in what direction. What's neat is Earth's population is huge, ~7.6 billion people, but both the birth and death rates are very small in comparison, about 4 and 2 people per second respectively. So we can use that to predict that Earth's population is overall increasing (direction) at a rate of ~2 people per second (speed).

share|cite|improve this answer

answered Jan 19 at 23:32

AEngineerAEngineer

1,5441317

share|cite|improve this answer

share|cite|improve this answer

answered Jan 19 at 23:32

AEngineerAEngineer

1,5441317

answered Jan 19 at 23:32

AEngineerAEngineer

1,5441317

answered Jan 19 at 23:32

AEngineerAEngineer

1,5441317

1,5441317

add a comment | 

add a comment | 

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