X/x-2 >= 0 equals x/x >= 0+2 simplified x >=2
Answer:
A
Step-by-step explanation:
Discriminant is given by
![D = b^{2} -4ac](https://tex.z-dn.net/?f=D%20%3D%20b%5E%7B2%7D%20-4ac)
If it is negative then in quadratic formula the square root part becomes negative which makes the solution complex.
so there cannot be any real solution if the Discriminant is negative or less than 0 ,
The correct option for the given question is
A
Question:
(a) How many bacteria would be found in 24 hours
(b) How many bacteria would be found in 2 days
(c) How long for 1000 bacteria to be found
Answer:
(a) 282429536481 bacteria
(b)
bacteria
(c) 6 days
Step-by-step explanation:
The question illustrates an exponential function
![y = ab^x](https://tex.z-dn.net/?f=y%20%3D%20ab%5Ex)
Where
![a = Initial\ Value = 1](https://tex.z-dn.net/?f=a%20%3D%20Initial%5C%20Value%20%3D%201)
--- i.e. triples
![x = number\ of\ hours](https://tex.z-dn.net/?f=x%20%3D%20number%5C%20of%5C%20hours)
Solving (a): Bacteria in 24 hours
In this case:
![x = 24](https://tex.z-dn.net/?f=x%20%3D%2024)
Substitute
,
and ![a = 1](https://tex.z-dn.net/?f=a%20%3D%201)
So:
![y = ab^x](https://tex.z-dn.net/?f=y%20%3D%20ab%5Ex)
![y = 1 * 3^{24](https://tex.z-dn.net/?f=y%20%3D%201%20%2A%203%5E%7B24)
![y = 1 * 282429536481](https://tex.z-dn.net/?f=y%20%3D%201%20%2A%20282429536481)
bacteria
Solving (b): Bacteria in 2 days
![2\ days =48\ hours](https://tex.z-dn.net/?f=2%5C%20days%20%3D48%5C%20hours)
So:
![x = 48](https://tex.z-dn.net/?f=x%20%3D%2048)
Substitute
,
and ![a = 1](https://tex.z-dn.net/?f=a%20%3D%201)
So:
![y = ab^x](https://tex.z-dn.net/?f=y%20%3D%20ab%5Ex)
![y = 1 * 3^{48](https://tex.z-dn.net/?f=y%20%3D%201%20%2A%203%5E%7B48)
bacteria
Solving (c): How long for 1000 bacteria
In this case:
![y = 1000](https://tex.z-dn.net/?f=y%20%3D%201000)
Substitute
,
and ![a = 1](https://tex.z-dn.net/?f=a%20%3D%201)
So:
![y = ab^x](https://tex.z-dn.net/?f=y%20%3D%20ab%5Ex)
![1000 = 1 *3^x](https://tex.z-dn.net/?f=1000%20%3D%201%20%2A3%5Ex)
![1000 = 3^x](https://tex.z-dn.net/?f=1000%20%3D%203%5Ex)
Take Log of both sides
![Log1000 = Log3^x](https://tex.z-dn.net/?f=Log1000%20%3D%20Log3%5Ex)
This gives:
![Log1000 = xLog3](https://tex.z-dn.net/?f=Log1000%20%3D%20xLog3)
Make x the subject
![x = \frac{Log1000}{Log3}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7BLog1000%7D%7BLog3%7D)
![x \approx 6](https://tex.z-dn.net/?f=x%20%5Capprox%206)
<em>Hence: It takes 6 days</em>
Answer:
2020
Step-by-step explanation: