The data below shows the number of birds spotted by a bird watcher each hour over 10 hours:
1 answer:
First, we always have to list them from least to greatest: 3,7,10,11,12,14,15,17,17,21.
A. I attached an image of the cumulative frequency table.
B. I wasn't able to make a histogram since I can't find any templates or programs to create it on.
Part C:
Mean: 12.7
Median: 26/2=13
Mode: 17
Range: 21 -3 = 18
Part D:
Minimum: 3
First Quartile: 10
Third Quartile: 17
Maximum: 21
E. I can't a program again, but I can help you over a call if you'd wish.
Part F:
40th Percentile: 0.31
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Answers:
- Exponential and increasing
- Exponential and decreasing
- Linear and decreasing
- Linear and increasing
- Exponential and increasing
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Explanation:
Problems 1, 2, and 5 are exponential functions of the form where b is the base of the exponent and 'a' is the starting term (when x=0).
If 0 < b < 1, then the exponential function decreases or decays. Perhaps a classic example would be to study how a certain element decays into something else. The exponential curve goes downhill when moving to the right.
If b > 1, then we have exponential growth or increase. Population models could be one example; though keep in mind that there is a carrying capacity at some point. The exponential curve goes uphill when moving to the right.
In problems 1 and 5, we have b = 2 and b = 1.1 respectively. We can see b > 1 leads to exponential growth. I recommend making either a graph or table of values to see what's going on.
Meanwhile, problem 2 has b = 0.8 to represent exponential decay of 20%. It loses 20% of its value each time x increases by 1.
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Problems 3 and 4 are linear functions of the form y = mx+b
m = slope
b = y intercept
This b value is not to be confused with the previously mentioned b value used with exponential functions. They're two different things. Unfortunately letters tend to get reused.
If m is positive, then the linear function is said to be increasing. The line goes uphill when moving to the right.
On the other hand if m is negative, then we go downhill while moving to the right. This line is decreasing.
Problem 3 has a negative slope, so it is decreasing. Problem 4 has a positive slope which is increasing.