1.Exam 2_865740278
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Big Bend Community College *
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Course
107
Subject
Mathematics
Date
Apr 3, 2024
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docx
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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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4.
Consider this data about COVID-19 from a DIFFERENT
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. 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 10,000 new cases. Rounding to the nearest whole number is fine.
Weeks since 10
th
Case
New Cases
0
2000
1
2900
2
4200
3
6100
4
8800
5.
Lastly, let’s pretend that we want to give our employees in total a 44% raise in the next two years, but we want to spread out a consistent percent raise over two years (
the same percent raise twice) to make this happen. Some justification for this could be: we can’t afford a 44% raise right now, but we don’t want to lose our employees to the competition, so we want to start the raise process right away.
b.
What consistent percent raise (
the same percent raise each year) should we give our employees each year to make our “in total a 44% raise in the next two years” happen? (Be accurate with an answer like 1.2%)