The numbers d (in millions) of drug prescriptions filled by independent outlets in the United States from 2000 through 2007 can be approximated by the model
d(t)= 10.6t + 699, 0 ≤ t ≤ 4
15.5t + 637, 5 ≤ t ≤ 7
where t represents the year, with t=0 corresponding to 2000.
Use this model to find the number of drug prescriptions filled by independent outlets in each year from 2000 through 2007.
what's the trouble? Just sub in the values. Just watch that you change which definition of d(t) you use for the portions of the domain.
year t d(t)
2000 0 10.6+0+699 = 699
2001 1 ...
...
2005 5 15.5*5+637 = 7145
2006 6 ...
...
To find the number of drug prescriptions filled by independent outlets in each year from 2000 through 2007 using the given model, we can substitute the corresponding values of t into the equation and solve for d(t). Let's calculate step-by-step:
Step 1: For the years 2000-2003 (0 ≤ t ≤ 4):
Substitute t values of 0, 1, 2, 3, and 4 into the equation d(t) = 10.6t + 699.
For t = 0:
d(0) = 10.6(0) + 699
d(0) ≈ 699
For t = 1:
d(1) = 10.6(1) + 699
d(1) ≈ 709.6
For t = 2:
d(2) = 10.6(2) + 699
d(2) ≈ 720.2
For t = 3:
d(3) = 10.6(3) + 699
d(3) ≈ 730.8
For t = 4:
d(4) = 10.6(4) + 699
d(4) ≈ 741.4
Therefore, the number of drug prescriptions filled by independent outlets for the years 2000-2003 (0 ≤ t ≤ 4) is approximately:
2000: 699 million
2001: 709.6 million
2002: 720.2 million
2003: 730.8 million
2004: 741.4 million
Step 2: For the years 2005-2007 (5 ≤ t ≤ 7):
Substitute t values of 5, 6, and 7 into the equation d(t) = 15.5t + 637.
For t = 5:
d(5) = 15.5(5) + 637
d(5) ≈ 712.5
For t = 6:
d(6) = 15.5(6) + 637
d(6) ≈ 728
For t = 7:
d(7) = 15.5(7) + 637
d(7) ≈ 743.5
Therefore, the number of drug prescriptions filled by independent outlets for the years 2005-2007 (5 ≤ t ≤ 7) is approximately:
2005: 712.5 million
2006: 728 million
2007: 743.5 million
In summary, the estimated number of drug prescriptions filled by independent outlets for each year from 2000 through 2007 is as follows:
2000: 699 million
2001: 709.6 million
2002: 720.2 million
2003: 730.8 million
2004: 741.4 million
2005: 712.5 million
2006: 728 million
2007: 743.5 million
To find the number of drug prescriptions filled by independent outlets in each year from 2000 through 2007, we need to substitute the values of t ranging from 0 to 7 into the given models.
Given models:
d(t) = 10.6t + 699, where 0 ≤ t ≤ 4
d(t) = 15.5t + 637, where 5 ≤ t ≤ 7
To find d(t) for each year, we can substitute the value of t into the equation and calculate the result.
For t = 0 (year 2000):
Using the first model, d(t) = 10.6 * 0 + 699 = 699
So, the number of drug prescriptions filled in the year 2000 is approximately 699 million.
For t = 1 (year 2001):
Using the first model, d(t) = 10.6 * 1 + 699 = 709.6
So, the number of drug prescriptions filled in the year 2001 is approximately 709.6 million.
For t = 2 (year 2002):
Using the first model, d(t) = 10.6 * 2 + 699 = 720.2
So, the number of drug prescriptions filled in the year 2002 is approximately 720.2 million.
For t = 3 (year 2003):
Using the first model, d(t) = 10.6 * 3 + 699 = 730.8
So, the number of drug prescriptions filled in the year 2003 is approximately 730.8 million.
For t = 4 (year 2004):
Using the first model, d(t) = 10.6 * 4 + 699 = 741.4
So, the number of drug prescriptions filled in the year 2004 is approximately 741.4 million.
For t = 5 (year 2005):
Using the second model, d(t) = 15.5 * 5 + 637 = 714.5
So, the number of drug prescriptions filled in the year 2005 is approximately 714.5 million.
For t = 6 (year 2006):
Using the second model, d(t) = 15.5 * 6 + 637 = 730
So, the number of drug prescriptions filled in the year 2006 is approximately 730 million.
For t = 7 (year 2007):
Using the second model, d(t) = 15.5 * 7 + 637 = 745.5
So, the number of drug prescriptions filled in the year 2007 is approximately 745.5 million.
Therefore, the estimated number of drug prescriptions filled by independent outlets for each year from 2000 through 2007 is as follows:
- 2000: Approximately 699 million
- 2001: Approximately 709.6 million
- 2002: Approximately 720.2 million
- 2003: Approximately 730.8 million
- 2004: Approximately 741.4 million
- 2005: Approximately 714.5 million
- 2006: Approximately 730 million
- 2007: Approximately 745.5 million