For this case we have the following function:
![S (t) = 3405.120e^{0.284t}](https://tex.z-dn.net/?f=S%20%28t%29%20%3D%203405.120e%5E%7B0.284t%7D)
By definition, the average rate of change is given by:
![Avr =\frac{S(t2) -S(t1)}{t2-t1}](https://tex.z-dn.net/?f=Avr%20%3D%5Cfrac%7BS%28t2%29%20-S%28t1%29%7D%7Bt2-t1%7D)
If t is the number of years since 2000, we have to:
For the year 2001 ![t1 = 1](https://tex.z-dn.net/?f=t1%20%3D%201)
For the year 2010 ![t2 = 10](https://tex.z-dn.net/?f=t2%20%3D%2010)
On the other hand:
![S (t2) = 3405.120e^{0.284*10}\\S (t2) = 3405.120e^{2.84}\\S (t2) = 58281](https://tex.z-dn.net/?f=S%20%28t2%29%20%3D%203405.120e%5E%7B0.284%2A10%7D%5C%5CS%20%28t2%29%20%3D%203405.120e%5E%7B2.84%7D%5C%5CS%20%28t2%29%20%3D%2058281)
While:
![S (t1) = 3405.120e^{0.284*1}\\ S (t1) = 3405.120e^{0.284}\\S (t1) = 4524](https://tex.z-dn.net/?f=S%20%28t1%29%20%3D%203405.120e%5E%7B0.284%2A1%7D%5C%5C%20S%20%28t1%29%20%3D%203405.120e%5E%7B0.284%7D%5C%5CS%20%28t1%29%20%3D%204524)
So, we have to:
![Avr =\frac{58281-4524}{10-1}](https://tex.z-dn.net/?f=Avr%20%3D%5Cfrac%7B58281-4524%7D%7B10-1%7D)
![Avr =\frac{53757}{9}\\Avr = 5973](https://tex.z-dn.net/?f=Avr%20%3D%5Cfrac%7B53757%7D%7B9%7D%5C%5CAvr%20%3D%205973)
So, the average rate of change is given by: 5973
Answer:
![Avr =5973\frac{millions-of-dollars}{year}](https://tex.z-dn.net/?f=Avr%20%3D5973%5Cfrac%7Bmillions-of-dollars%7D%7Byear%7D)
Answer:
![\boxed{B. \: 5 {x}^{6} + 5 {x}^{5} + 8 {x}^{2} - x + 2}](https://tex.z-dn.net/?f=%20%5Cboxed%7BB.%20%5C%3A%205%20%7Bx%7D%5E%7B6%7D%20%20%2B%205%20%7Bx%7D%5E%7B5%7D%20%20%2B%208%20%7Bx%7D%5E%7B2%7D%20%20-%20x%20%2B%202%7D%20)
Step-by-step explanation:
![= > (2 {x}^{6} + 8 {x}^{2} - x + 1) + (3 {x}^{6} + 5 {x}^{5} + 1) \\ \\ = > 2 {x}^{6} + 8 {x}^{2} - x + 1 + 3 {x}^{6} + 5 {x}^{5} + 1 \\ \\ = > 2 {x}^{6} + 3 {x}^{6} + 5 {x}^{5} + 8 {x}^{2} - x + 1 + 1 \\ \\ = > 5 {x}^{6} + 5 {x}^{5} + 8 {x}^{2} - x + 2](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20%282%20%7Bx%7D%5E%7B6%7D%20%20%2B%208%20%7Bx%7D%5E%7B2%7D%20-%20x%20%2B%201%29%20%2B%20%283%20%7Bx%7D%5E%7B6%7D%20%2B%205%20%7Bx%7D%5E%7B5%7D%20%20%2B%201%29%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3E%202%20%7Bx%7D%5E%7B6%7D%20%20%2B%208%20%7Bx%7D%5E%7B2%7D%20-%20x%20%2B%201%20%2B%203%20%7Bx%7D%5E%7B6%7D%20%2B%205%20%7Bx%7D%5E%7B5%7D%20%20%2B%201%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3E%202%20%7Bx%7D%5E%7B6%7D%20%20%2B%203%20%7Bx%7D%5E%7B6%7D%20%20%2B%205%20%7Bx%7D%5E%7B5%7D%20%20%2B%208%20%7Bx%7D%5E%7B2%7D%20%20-%20x%20%2B%201%20%2B%201%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3E%205%20%7Bx%7D%5E%7B6%7D%20%20%2B%205%20%7Bx%7D%5E%7B5%7D%20%20%2B%208%20%7Bx%7D%5E%7B2%7D%20%20-%20x%20%2B%202)
The unit rate meant the slope, which is represented by m in y=mx+b
First we must isolate the y by dividing both sides by -1 to get:
y=-x/7 or y=(-1/7)x, so the the unit rate is -1/7 or B
Hope this helps :)
1 gallon = 3.8 liters
multiplying both side by 91
91 gallons = 345.8 liters
please mark as brainliest