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Mathematics

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Apr 3, 2024

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Math 107. Exam 2 Growth. Always show support. Name:________________________________________ Don’t round for accuracy. 1. Pretend that in a certain city the number of new cases of COVID was reported to be 2000 new cases on Sunday. Let’s pretend that the number of new cases grows by 12% on Monday, grows by 8% on Tuesday, and then falls 8% on Wednesday, and finally falls again 12% on Thursday. a. What will the number of new cases be on Thursday after all of this growing and falling? (don’t round for accuracy) b. Most Americans think 12% up, 8% up, 8% down, and 12% down make a zero% change. Or does it... What is the total net change from Sunday to Thursday as a percent? (don’t round for accuracy)

2. You may have heard that inflation is getting better but this year the yearly inflation rate was 6% (meaning things became 6% more expensive over the course of the year). And the year before that the yearly inflation rate was 5% (meaning things became 5% more expensive over the course of that year). So because of inflation things got 5% more expensive and then 6% more expensive. Yikes! a. If an item costs $5,000 now, how much did it cost two years ago before all that inflation?

3. Consider this data about COVID-19 from a certain city. a) Make a table with Weeks since 10 th Case in the first column and New Covid Cases in the second column. Screenshot in the data table. b) Make a scatterplot with line/curve of best fit (choose the best option visually). Screenshot in the scatterplot. (note: one exam question has linear growth, while another exam question has exponential growth. Choose the best model visually for the exam question. You may want to do next exam question first to confirm your choice. Tip: one exam question has an obvious curve to it.) c) Write a linear/exponential equation that models this situation (consistent with your choice above). Time is the explanatory variable, and New Covid Cases is the response variable. d) Explain what the slope/multiplier (consistent with your choice above) means in this context of the problem. Be sure to use units and to write a clear sentence. e) Use your model to predict when there will be 1,000 new cases. Weeks since 10 th Case New Cases 0 2000 1 1850 2 1650 3 1500 4 1300

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