Birth Rate with limits, slopes, and derivatives

[john3j]

Hello everyone,

I am having a problem understanding a question about Birth rate in my Calculus I course. I am not asking anyone to do the work for me, but to guide me in the right direction or give me examples so that I can understand.

Here is the problem...

Patterns of fertility changed in India from 1970 to 2000 according to the equation y=-0.068x+5.22, where x is the number of years after 1970 and y is the average number of children per woman.
a) What number is f(30) and what does it represent?
b) What number is f'(30) and what does it represent?

I think that basically you would plug 30 in for x to give you 3.18, which is the average number of children per woman. I do not know what the difference is between f(30) and f'(30)? Any clarification would be greatly appreciated!

Thanks,
John

 

[wjm11]

Hello everyone,

I am having a problem understanding a question about Birth rate in my Calculus I course. I am not asking anyone to do the work for me, but to guide me in the right direction or give me examples so that I can understand.

Here is the problem...

Patterns of fertility changed in India from 1970 to 2000 according to the equation y=-0.068x+5.22, where x is the number of years after 1970 and y is the average number of children per woman.
a) What number is f(30) and what does it represent?
b) What number is f'(30) and what does it represent?

I think that basically you would plug 30 in for x to give you 3.18, which is the average number of children per woman. I do not know what the difference is between f(30) and f'(30)? Any clarification would be greatly appreciated!

Thanks,
John

The notation f' means the derivative of the function f. For part b you must find the derivative of the given equation. Hint: the given equation is a line. Derivatives of functions give slopes. Lines have constant slopes.

 

[john3j]

So are you saying that y=-0.068x+5.22 is the same as f(x)=-0.068x+5.22? For part a would I just do f(30)=-0.068(30)+5.22 and simplify? For part b would the derivative of y be dy/dx=-0.068? This is the slope you are referring to?

Thanks,
John

The notation f' means the derivative of the function f. For part b you must find the derivative of the given equation. Hint: the given equation is a line. Derivatives of functions give slopes. Lines have constant slopes.

 

[wjm11]

So are you saying that y=-0.068x+5.22 is the same as f(x)=-0.068x+5.22? For part a would I just do f(30)=-0.068(30)+5.22 and simplify? For part b would the derivative of y be dy/dx=-0.068? This is the slope you are referring to?

Thanks,
John

Yes. However, you must still interpret the meaning of the slope (particularly the negative sign, I would think).

 

[HallsofIvy]

Hello everyone,

I am having a problem understanding a question about Birth rate in my Calculus I course. I am not asking anyone to do the work for me, but to guide me in the right direction or give me examples so that I can understand.

Here is the problem...

Patterns of fertility changed in India from 1970 to 2000 according to the equation y=-0.068x+5.22, where x is the number of years after 1970 and y is the average number of children per woman.
a) What number is f(30) and what does it represent?
b) What number is f'(30) and what does it represent?

I think that basically you would plug 30 in for x to give you 3.18, which is the average number of children per woman.

The average number of children when? That is, what does the "30" represent?

I do not know what the difference is between f(30) and f'(30)? Any clarification would be greatly appreciated!

Thanks,
John

You should have learned that the derivative of a function is its "rate of change". Since f gives the number of children, f' shows how the number of children is changing per year.