Answer:
9990 years
Step-by-step explanation:
The exponential function with given values filled in can be solved for the unknown using logarithms.
__
Q(t) = 12 = 36e^(-0.00011t)
1/3 = e^(-0.00011t) . . . . . . divide by 36
ln(1/3) = -0.00011t . . . . . . take natural logs
t = ln(1/3)/(-0.00011) . . . . divide by the coefficient of t
t ≈ 9990 . . . years
Answer:
Classical probability
Step-by-step explanation:
- Classical property is that type of probability or statistical concept that deals with the measurement of the odds or likelihood of some event.
- It is that form of probability that is simplest in approach and includes the equal likelihood of happening or occurrence of an event.
- In order to determine the numerical probability of an event, it makes use of the knowledge of sample spaces in contrast with the observations.
- It takes a proper note of an event in order to calculate its probability and also it deals with the likelihood of a certain event rather than making observations.
Part A:
Given

defined by


but

Since, f(xy) ≠ f(x)f(y)
Therefore, the function is not a homomorphism.
Part B:
Given

defined by

Note that in

, -1 = 1 and f(0) = 0 and f(1) = -1 = 1, so we can also use the formular


and

Therefore, the function is a homomorphism.
Part C:
Given

, defined by


Since, f(x+y) ≠ f(x) + f(y), therefore, the function is not a homomorphism.
Part D:
Given

, defined by


but

Since, h(ab) ≠ h(a)h(b), therefore, the funtion is not a homomorphism.
Part E:
Given

, defined by
![\left([x_{12}]\right)=[x_4]](https://tex.z-dn.net/?f=%5Cleft%28%5Bx_%7B12%7D%5D%5Cright%29%3D%5Bx_4%5D)
, where
![[u_n]](https://tex.z-dn.net/?f=%5Bu_n%5D)
denotes the lass of the integer

in

.
Then, for any
![[a_{12}],[b_{12}]\in Z_{12}](https://tex.z-dn.net/?f=%5Ba_%7B12%7D%5D%2C%5Bb_%7B12%7D%5D%5Cin%20Z_%7B12%7D)
, we have
![f\left([a_{12}]+[b_{12}]\right)=f\left([a+b]_{12}\right) \\ \\ =[a+b]_4=[a]_4+[b]_4=f\left([a]_{12}\right)+f\left([b]_{12}\right)](https://tex.z-dn.net/?f=f%5Cleft%28%5Ba_%7B12%7D%5D%2B%5Bb_%7B12%7D%5D%5Cright%29%3Df%5Cleft%28%5Ba%2Bb%5D_%7B12%7D%5Cright%29%20%5C%5C%20%20%5C%5C%20%3D%5Ba%2Bb%5D_4%3D%5Ba%5D_4%2B%5Bb%5D_4%3Df%5Cleft%28%5Ba%5D_%7B12%7D%5Cright%29%2Bf%5Cleft%28%5Bb%5D_%7B12%7D%5Cright%29)
and
![f\left([a_{12}][b_{12}]\right)=f\left([ab]_{12}\right) \\ \\ =[ab]_4=[a]_4[b]_4=f\left([a]_{12}\right)f\left([b]_{12}\right)](https://tex.z-dn.net/?f=f%5Cleft%28%5Ba_%7B12%7D%5D%5Bb_%7B12%7D%5D%5Cright%29%3Df%5Cleft%28%5Bab%5D_%7B12%7D%5Cright%29%20%5C%5C%20%5C%5C%20%3D%5Bab%5D_4%3D%5Ba%5D_4%5Bb%5D_4%3Df%5Cleft%28%5Ba%5D_%7B12%7D%5Cright%29f%5Cleft%28%5Bb%5D_%7B12%7D%5Cright%29)
Therefore, the function is a homomorphism.
Answer:
B and D
Step-by-step explanation:

Answer:
Step-by-step explanation:
11.04 = 10(1.02)^n
1.104 = 1.02^n
ln 1.104 = ln 1.02^n
ln 1.104 = n ln 1.02
n = ln 1.104/ ln 1.02
n = 4.99630409516
4.99 can be rounded to 5.
So a reasonable domain would be 0 ≤ x < 5
PART B)
f(0) = 10(1.02)^0
f(0) = 10(1)
f(0) = 10
The y-intercept represents the height of the plant when they began the experiment.
f(1) = 10(1.02)^1
f(1) = 10(1.02)
f(1) = 10.2
(1, 10.2)
f(5) = 10(1.02)^5
f(5) = 10(1.1040808)
f(5) = 11.040808
f(1)=10(1.02)^1
f(1)=10.2
Average rate= (fn2-fn1)/(n2-n1)
=11.04-10.2/(5-1)
=0.22
the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.