I need help help filling out this study guide for math function for my final! pl

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I need help help filling out this study guide for math function for my final! please help if you can!

As of 2012, there were over 1 billion Facebook users in the world. But Facebook wasn't always such an internet giant: 6 months after starting, they had a whopping 0.13 million users. Consider the following data about the number of users in Facebook's early days, which defines the total number of Facebook users F as a function of the number of months m since the company launched in late 2003 Months since 1 Facebook users [in millions 0.13 1.0 2003, mn 36 56 59.3 59.5 2.0 100.0 130.0 140.0 Problem 5. Use the average rate of change to estimate the number of Facebook users after 4 years (48 months). (a) 48 million Facebook users (b) 50 million Facebook users (c) 55.6 million Facebook users (d) 56 million Facebook users (e) 64.8 million Facebook users (f) 68 million Facebook users (g) 69.3 million Facebook users Problem 6. Suppose that, from rn = 59.5 to m = 60 months, the average rate of change of F = F(m) is 60 million users per month. Which of the following can we conclude from this? (a) The number of Facebook users at the end of 60 months is 60 million users. (b) The number of Facebook users at the end of 60 months is 30 million users. (c) The number of Facebook users at the end of 60 months is 170 million users. (d) The number of Facebook users at the end of 60 months is 200 million users. (e) The number of Facebook users at the end of 60 months is 140 million users. (f) None of the above. Problem 7. Is F-F(n) concave down or concave up from m = 6 months to m = 59.5 months? (a) Concave down (b) Concave up (c) No concavity (d) Not enough information provided Problem 8. Explain your response to the previous question: (a) Because F is decreasing (b) Because F is increasing (c) Because the average rate of change of F = F(m) is decreasing (d) Because the average rate of change of F = F(m) is increasing (e) None of these explanations are relevant to concavity Problem9. Which of the following interpretations is appropriate for this situation? (a) The number of Facebook users continues to decline, but this decline is smaller and smaller as time passes, (b) The number of Facebook users continues to decline, and this decline is greater and greater as time passes. (c) The number of Facebook users continues to grow, but this growth is smaller and smaller as time passes.

Explanation / Answer

5. Users after 36 months = 12 million

Change from 36 to 56 months = 100-12= 88 million

Average rate of change = 88/20=4.4 million

Estimated users at 48 months = 12+4.4x12=64.8 million

So option (e) is correct.

6. Average rate of change = 60 million per month

So change from 59.5 to 60 month = 0.5x60= 30 million

Users after 59.5 months = 140 million

So we can conclude that number of users at the end of 60 months = 140+30=170 million

Option (c) is correct

7. F (m) is concave up, so option (b) is correct.

8. Average rate of change of F is increasing, so option (d) is correct.

9. Option (d) is correct, the number of Facebook users continues to grow and the growth is greater and greater as time passes.

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