Solve all parts and show work please! Thank you!! The graph below represents the

Question

Solve all parts and show work please! Thank you!!

The graph below represents the growth of a certain population. The population P is measured in thousands of people and time t is measured in years. Use the graph to answer the following questions. Estimate the initial population. Use function notation to express your answer. Show the work necessary to estimate the average rate of change in the population from year 2 to year 3. Illustrate on the graph above. Interpret this value in context of the problem. Estimate P'(4). Illustrate on the graph above. Interpret this value in context of the problem. What is the limiting value of the population? Express your answer as an appropriate limit. What is the limiting value of the rate of change in the population? Express your answer as an appropriate limit.

Explanation / Answer

(a) 5000

(b)10500

(c)p'(4)=(p(5)-p(4))/(5-3)=(12000-11000)/2=500

(d) when time t tends to infinity Population P=12000

(e)Rate of change of population when t tends to infinity is zero since slope is zero

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