The correct answer is the 2.4
The constant in an equation is the number(s) that don't have variables.
This is because variables can change the number they are attached to, making them not constant.
Hope this helps!
Answer:
hi
Step-by-step explanation:
The function f(x) = 4(4)x represents the growth of a fly population every year in a remote swamp.
calculates three times a year, not just once a year.
![f(x)= 4(4)^x](https://tex.z-dn.net/?f=f%28x%29%3D%204%284%29%5Ex)
3 times a year
so x becomes 3x
![f(x)= 4(1+r)^{3x}](https://tex.z-dn.net/?f=f%28x%29%3D%204%281%2Br%29%5E%7B3x%7D)
![4(4)^x=4(1+r)^{3x}](https://tex.z-dn.net/?f=4%284%29%5Ex%3D4%281%2Br%29%5E%7B3x%7D)
Take log on both sides
![log(4)^x=log(1+r)^{3x}](https://tex.z-dn.net/?f=log%284%29%5Ex%3Dlog%281%2Br%29%5E%7B3x%7D)
![log(4)^x=log(1+r)^{3x}](https://tex.z-dn.net/?f=log%284%29%5Ex%3Dlog%281%2Br%29%5E%7B3x%7D)
Use log property and move exponent before log
![xlog(4)=3xlog(1+r)}](https://tex.z-dn.net/?f=xlog%284%29%3D3xlog%281%2Br%29%7D)
Divide both sides by x
log 4 = 3 log(1+r)
Solve for '1+r'
log 4 = log(1+r)^3
Remove log from both sides
4 = (1+r)^3
take cube root on both sides
1.584740= 1+r
1+r = 1.59
![f(x)= 4(1+r)^{3x}](https://tex.z-dn.net/?f=f%28x%29%3D%204%281%2Br%29%5E%7B3x%7D)
so equation becomes
![f(x)= 4(1.59)^{3x}](https://tex.z-dn.net/?f=f%28x%29%3D%204%281.59%29%5E%7B3x%7D)
1+r = 1.59
subtract 1 from both sides
So r= 59 = 59%
So growth factor is 59%
Answer is option C
Answer:
Mean = 30.68
Standard deviation = 6.095
Two standard deviations above the mean = 42.87
Step-by-step explanation:
Given the following data :
21; 21; 22; 23; 24; 24; 25; 25; 28; 29; 29; 31; 32; 33; 33; 34; 35; 36; 36; 36; 36; 38; 38; 38; 40
Mean = Σ(x) / n
n = 25
Σ (X) = 767
Mean (m) = 767 / 25
Mean (m) = 30.68
Standard deviation : sqrt[Σ(x - m) / n]
Using a calculator :
Standard deviation = 6.095 ( 2 decimal places)
2 standard deviations above the mean :
Mean + 2(standard deviation)
Mean + 2(6.095)
30.68 + 12.19
30.68 + 12.19
= 42.87
Answer:
The function g(x) increases faster than the function f(x)