The population of the bacteria 96 minutes from now is 12.
Answer:
1. ![m = 2n](https://tex.z-dn.net/?f=m%20%3D%202n)
2. ![m = 3n + 1](https://tex.z-dn.net/?f=m%20%3D%203n%20%2B%201)
Step-by-step explanation:
1. 8 = 4 * 2; 10 = 5 * 2; 18 = 9 * 2....
2. 4 = 1 * 3 + 1; 7 = 2 * 3 + 1; 10 = 3 * 3 + 1....
<em>90</em> and all of its multiples are.
Answer:
<em>The least number of items to produce is 41</em>
Step-by-step explanation:
<u>Average Cost</u>
Given C(x) as the cost function to produce x items. The average cost is:
![\displaystyle \bar C(X)=\frac{C(x)}{x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbar%20C%28X%29%3D%5Cfrac%7BC%28x%29%7D%7Bx%7D)
The cost function is:
![C(x) = -20x+1681](https://tex.z-dn.net/?f=C%28x%29%20%3D%20-20x%2B1681)
And the average cost function is:
![\displaystyle \bar C(X)=\frac{-20x+1681}{x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbar%20C%28X%29%3D%5Cfrac%7B-20x%2B1681%7D%7Bx%7D)
We are required to find the least number of items that can be produced so the average cost is less or equal to $21.
We set the inequality:
![\displaystyle \frac{-20x+1681}{x}\le 21](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B-20x%2B1681%7D%7Bx%7D%5Cle%2021)
Multiplying by x:
![-20x+1681 \le 21x](https://tex.z-dn.net/?f=-20x%2B1681%20%5Cle%2021x)
Note we multiplied by x and did not flip the inequality sign because its value cannot be negative.
Adding 20x:
![1681 \le 21x+20x](https://tex.z-dn.net/?f=1681%20%5Cle%2021x%2B20x)
![1681 \le 41x](https://tex.z-dn.net/?f=1681%20%5Cle%2041x)
Swapping sides and changing the sign:
![41x \ge 1681](https://tex.z-dn.net/?f=41x%20%5Cge%201681)
Dividing by 41:
![x\ge 41](https://tex.z-dn.net/?f=x%5Cge%2041)
The least number of items to produce is 41