The possible four options for qustion \"b\" are 1. 30 - 50 2. 0- 50 3. 0-25 4.25

Question

The possible four options for qustion "b" are
1. 30 - 50
2. 0- 50
3. 0-25
4.25-50

Populations starting out in closed environments grow slowly at first, when there are relatively few members, then more rapidly as the number of reproducing individuals increases and resources are still abundant, then slowly again as the population reaches the carrying capacity of the environment. 35 300 200 Answer parts a and b below, 0 40 20 Time (days) 30 50 a. Use graphical techniques to graph the derivative of the fruit fly population, using the given graph of the population. Choose the correct graph of the derivative. A. 0 1020 30 40 50 Time (days) 0 1020 30 40 50 Time (days) 0 1020 30 40 50 Time (days) 0 1020 3040 50 Time (days) b. During what days does the population seem to be increasing fastest? Slowest? Fill in the blanks The population seems to increase fastest during days I and slowest during days

Explanation / Answer

(a) Graph of derivative, we need to draw tangent at every point nd see the nature of tangent.

So, we will check slope between 20 to 30

(20,100) and (30,250)

Slope=15

So, max value of derivative graph should be 15

So, C is correct option because here maximum is 15

(b) Fastest at t=215 because here we got max vaue of derivative i,e 15

According to graph we can see slowest at t=50

So, 4 is correct option

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