The first graph shows the size of a population of Florida panthers as a function of time, where x represents the number of years after 1980. The following two graphs show the same graph, including a tangent line at various points.

a)Estimate the number of panthers in 1985 and 1996.

b)At what rate was the population decreasing in 1986 and 1991?

c)Estimate the time at which the panther population was decreasing the fastest.

How to get the exact answer instead of just guessing on graph?

Question

The first graph shows the size of a population of Florida panthers as a function of time, where x represents the number of years after 1980. The following two graphs show the same graph, including a tangent line at various points. 

a)Estimate the number of panthers in 1985 and 1996. 

b)At what rate was the population decreasing in 1986 and 1991? 

c)Estimate the time at which the panther population was decreasing the fastest. 

How to get the exact answer instead of just guessing on graph?

ranga · Answer

Are you going to post the graphs?

anonymous · Answer

attachment

anonymous · Answer

attached are the graphs

anonymous · Answer

I kinda know the answers just wanted to know about the steps to arrive at the answers

ranga · Answer

Reading from a graph, unless it passes through the corners of a square in the graph sheet, is going to be an estimate.  That is the reason they say in a) ESTIMATE

ranga · Answer

a) 
1985 ~ 99
1996 ~ 41

ranga · Answer

b) In 1986 the population was decreasing at the rate of 5.98 per year (from the slope on the graph) but it should be rounded to about 6 panthers per year.
In 1991 the population was decreasing at the rate of 5.6 per year rounded to about 6 panthers per year.

ranga · Answer

c) The last one is a bit tough to read from the graph.  The point the rate of decrease is the fastest will be the point on the first graph where the tangent is the steepest. It is also the point at which the graph changes from concave down to concave up.  It could be 1988, 1989 or 1990.  So I will choose the midpoint as the average: 1989.

ranga · Answer

What to they say are the answers?

anonymous · Answer

a)1985=98, 1986=41 
b)1986:decrease of 5.98 panthers
1991: decrease of 5.6 panthers
c)1987-1999, so its 1988

ranga · Answer

Okay.  Since it is an estimate my answers should be acceptable for a and c.
For b, normally when counting people or animals or fishes the numbers will be rounded because there are no fractional people or animals.  Even though the graph specifies the exact values of slope as 5.98 and 5.6, it wouldn't be a bad idea to round them to the nearest whole number because the number refers to the decrease in the number of panthers.