Question

The number of new businesses established in the US since 1990 can be modeled by the function N(x)=110.8x^3-5305.5x^2+76,701x+332,892 where x = 0 represents 1990 and the domain is [0, 25].

1. According to the model, about how many new businesses were established in 2011? Don’t forget to label and interpret the answer.

2. What was the average rate of change in the number of new businesses established between 2000 and 2010? Don’t forget to label and interpret the answers.

3. What is the instantaneous rate of change in the number of new businesses established in 2011? Remember to label and interpret the answer.

4. Consider the year 2015 (x = 25). Evaluate D(25),D’(25),and D’’(25). Label and interpret the meaning of each answer.

5. Use the First Derivative Test to determine the extrema of the function on the given domain. Classify as max/min and absolute/relative. For what intervals does the function increase/decrease? Please label and interpret each answer in the context of this problem.

6. Use the Second Derivative Test to discuss the concavity of this function on the given interval. What is the POI? Interpret the meaning of the POI in the context of this problem.

Answer 1

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