Answer: Sheldon babysat for 6 hours on Saturday.
Step-by-step explanation:
Let x represent the number of hours that Sheldon babysat on Saturday.
He babysat for Saturday and Sunday. If Sheldon babysat for 8 hours on Sunday, it means that the total number of hours that he babysat during the weekend was
(8 + x) hours.
Seldon gets paid $4 per hour to baby sit his cousins. It means that the total amount that he earned during the weekend was 4(8 + x)
He made a total of $56. Therefore,
4(8 + x) = 56
8 + x = 56/4 = 14
x = 14 - 8
x = 6 hours
Answer:
![n = 500e^{-4.1589x}](https://tex.z-dn.net/?f=n%20%3D%20500e%5E%7B-4.1589x%7D)
Step-by-step explanation:
Using the exponential growth equation
where;
N₀ is the initial population of the bacteria
N(t) is the population of the bacteria during time t
If a biologist puts an initial population of 500 bacteria into a growth plate, this means that N₀ = 500 at t = 0
![N(t) = N_0e^{-kt}\\N(t) = 500e^{-k(0)}\\N(t) = 500e^0\\N(t) = 500](https://tex.z-dn.net/?f=N%28t%29%20%3D%20N_0e%5E%7B-kt%7D%5C%5CN%28t%29%20%3D%20500e%5E%7B-k%280%29%7D%5C%5CN%28t%29%20%3D%20500e%5E0%5C%5CN%28t%29%20%3D%20500)
If the population is expected to double every 4 hours, this means when t = 4, N₀ = 2(500) = 1000
![N(t) = N_0e^{-kt}\\500 = 1000e^{-4k}\\\frac{500}{1000} = e^{-4k}\\0.5 = e^{-4k}\\ln(0.5) = lne^{-4k}\\ln(0.5) = -4k\\k = \frac{ln0.5}{-4} \\k = 0.1733](https://tex.z-dn.net/?f=N%28t%29%20%3D%20N_0e%5E%7B-kt%7D%5C%5C500%20%3D%201000e%5E%7B-4k%7D%5C%5C%5Cfrac%7B500%7D%7B1000%7D%20%3D%20%20e%5E%7B-4k%7D%5C%5C0.5%20%3D%20e%5E%7B-4k%7D%5C%5Cln%280.5%29%20%3D%20lne%5E%7B-4k%7D%5C%5Cln%280.5%29%20%3D%20-4k%5C%5Ck%20%3D%20%5Cfrac%7Bln0.5%7D%7B-4%7D%20%5C%5Ck%20%3D%200.1733)
The equation that will give the expected number of bacteria, n, after x days, can be gotten by substituting N(t) = n and t = x days = 24x hours
![N(t) = N_0e^{-kt}\\n = N_0e^{-0.1733(24x)}\\n = 500e^{-4.1589x}](https://tex.z-dn.net/?f=N%28t%29%20%3D%20N_0e%5E%7B-kt%7D%5C%5Cn%20%3D%20N_0e%5E%7B-0.1733%2824x%29%7D%5C%5Cn%20%3D%20500e%5E%7B-4.1589x%7D)
<em>Hence the equation that will give the expected number of bacteria, n, after x days is </em>![n = 500e^{-4.1589x}](https://tex.z-dn.net/?f=n%20%3D%20500e%5E%7B-4.1589x%7D)
I wasn’t sure if I should include all the numbers if they were doubles but you get the idea. Hope this helps!
Hey!
When you raise a number to a power, you multiply that number by itself. (4^2 = 4 * 4 for example) 1.2 * 1.2 = 1.44 That's for the first one.
2^3 + 17 - 3 * 4. ---> 8 + 17 - 3 * 4
8 + 17 - 3 * 4 ---> 8 + 17 - 12
8 + 17 - 12 ---> 25 - 12
25 - 12 ---> 13 Thats for the second one.
9^2 / 3^3 ---> 81/27
81/27 ---> 3 Thats for the third one.
Hope this helps!! ☺♥
Answer:
12.5 !!!!
Step-by-step explanation: