Explanation: Part A:
Denote x as the year, which is the independent variable and y as the number of deaths due to opioid overdose.
If 1999 is year 0, then the first available value of x is, x_{1} = 0. Corresponding value of y is, y_{1} = 8,280.
Now, 2015 – 1999 = 16. So, if value of x is 0 for 1999, value of x will be 16 for 2015.
Thus, the second available value of x is, x_{2} = 16. Corresponding value of y is, y_{2} = 33,092.
Now, an exponential model is of the form: y = ab^{x}. Using the values above, a and b can be found as follows, thus creating the model:
Average yearly percent change:
In the exponential model of the above form: y = ab^{x}, “b” is commonly referred to as the “growth factor”. If b < 1, then there is a reduction or decay over time, whereas if b > 1, then there is a growth or increase over time.
For b > 1, that is, in case of growth, b can be expressed as, b = 1 + r, where r is the percentage or proportion of growth, attained over each unit increase in time.
Here, b = 1.09, that is, 1 + r = 1.09; r = 0.09 = 9% (= 0.09 × 100%).
Thus, the average yearly percent change from 1999 to 2015 is approximately 9%.
Extrapolation for 2020:
The year 2020 is 5 years from 2015, which is the year 16. So, for 2020, x = 21 (= 16 + 5). Substitute thi...
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