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?
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 then just find the slope of the secant line which passes through two points near the point on the curve.
I'm not sure what you mean by 'tangent line coordinates.' A tangent line is represented by an equation . 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?
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
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.