1. ## Instantaneous rate

I need to know how to estimate the instantaneous rate of population growth of a month. In the previous question i was asked to find the average rare of population growth which i believe would be to just find the slope. ( Is that correct?

In order to find the instantaneous rate of population growth of a month I believe you have to find the slope of the tangent line. so do I just find a tangent line and estimate to coordinates and use the slope fomula?

When i did this i got a fraction of 70/8. Can ths slope be a fracton when it comes to population growth?

2. Originally Posted by asweet1
I need to know how to estimate the instantaneous rate of population growth of a month. In the previous question i was asked to find the average rare of population growth which i believe would be to just find the slope. ( Is that correct?

In order to find the instantaneous rate of population growth of a month I believe you have to find the slope of the tangent line. so do I just find a tangent line and estimate to coordinates and use the slope fomula?

When i did this i got a fraction of 70/8. Can ths slope be a fracton when it comes to population growth?
what are you working with, a table of values?

how did you arrive at 70/8 ? more problem info, please.

3. Originally Posted by asweet1
I need to know how to estimate the instantaneous rate of population growth of a month. In the previous question i was asked to find the average rare of population growth which i believe would be to just find the slope. ( Is that correct?

In order to find the instantaneous rate of population growth of a month I believe you have to find the slope of the tangent line so do I just find a tangent line and estimate to coordinates and use the slope fomula?

When i did this i go a fraction of 70/8. Can ths slope be a fracton when it comes to population growth?
Yes, you are correct about the instantaneous rate. That's just the derivative. I'm not sure what you're asking after that (in red). I assume you have a population growth curve of some kind. If you want to approximate the slope of a tangent line around a certain point $\displaystyle (x,y)$ then just find the slope of the secant line which passes through two points near the point $\displaystyle (x,y)$ on the curve.

4. So once i find the slope of the secant line how do i incororate it into the tangent line coordinates i found?

5. To skeeter i am working with a graph i got 70/8 by finding p'(22)= p(22)-P(14)/22-14 which equals to 380-310/22-14

6. Originally Posted by asweet1
So once i find the slope of the secant line how do i incororate it into the tangent line coordinates i found?
I'm not sure what you mean by 'tangent line coordinates.' A tangent line is represented by an equation $\displaystyle \Delta y=y'\Delta x$. It's not represented by a pair of coordinates. I think you may be referring to the point of tangency.

Could you provide the exact wording of the problem you're working on? What is the function?

7. A small lake is stocked with trout in the early sprin of 2005. The population of trout in the lake (where t is measured in months) is shown below. (it shows a graph)

(a) what is the average rate of population growth bewtween month 10 and month 20?

-Here i would find the slope

(b) Estimate the instantaneous rate of population growth month 22.

-Here i am not sure what to do exactly

8. It's not easy to help without the graph. But I'll give you a brief tip.

Find two points, one on each side, of the point at t=22 months. Chose the points so that they are very close to the point at t=22 months. Draw a line through these points. The equation of the line through the points will be the approximation you're looking for.