Answer: 7300
Step-by-step explanation: 5200 - 4000 = 1200. 1200 divided by four hours is 300. So 300 bacteria grow per hour. Then you multiply 300 by 11 hours and get 3300 bacteria plus the starting 4000 and your final number is 7300
Step-by-step explanation:
Add all the data and divide by 2 to get your median
Answer:
![3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n](https://tex.z-dn.net/?f=3%20%2B%2012%20%2B%2048%20%2B%20192%20%2B%20768%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%203%20%2A%204%5En)
![4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n](https://tex.z-dn.net/?f=4%20%2B%2032%20%2B%20256%20%2B%202048%20%2B%2016384%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%204%20%2A%208%5En)
![2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n](https://tex.z-dn.net/?f=2%20%2B%206%20%2B%2018%20%2B%2054%20%2B%20162%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%202%2A%203%5En)
![3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n](https://tex.z-dn.net/?f=3%20%2B%2015%20%2B%2075%20%2B%20375%20%2B%201875%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%203%2A%205%5En)
Step-by-step explanation:
Given
See attachment for complete question
Required
Match equivalent expressions
Solving (a):
![3 + 12 + 48 + 192 + 768](https://tex.z-dn.net/?f=3%20%2B%2012%20%2B%2048%20%2B%20192%20%2B%20768)
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
![3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n](https://tex.z-dn.net/?f=3%20%2B%2012%20%2B%2048%20%2B%20192%20%2B%20768%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%203%20%2A%204%5En)
Solving (b):
![4 + 32 + 256 + 2048 + 16384](https://tex.z-dn.net/?f=4%20%2B%2032%20%2B%20256%20%2B%202048%20%2B%2016384)
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
![4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n](https://tex.z-dn.net/?f=4%20%2B%2032%20%2B%20256%20%2B%202048%20%2B%2016384%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%204%20%2A%208%5En)
Solving (c):
![2 + 6 + 18 + 54 + 162](https://tex.z-dn.net/?f=2%20%2B%206%20%2B%2018%20%2B%2054%20%2B%20162)
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
![2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n](https://tex.z-dn.net/?f=2%20%2B%206%20%2B%2018%20%2B%2054%20%2B%20162%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%202%2A%203%5En)
Solving (d):
![3 + 15 + 75 + 375 + 1875](https://tex.z-dn.net/?f=3%20%2B%2015%20%2B%2075%20%2B%20375%20%2B%201875)
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
![3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n](https://tex.z-dn.net/?f=3%20%2B%2015%20%2B%2075%20%2B%20375%20%2B%201875%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%203%2A%205%5En)
A = 1/2(4)(6.9)
A = 27.6 / 2
A = 13.8
answer
13.8 cm^2