Answer:
1) The size of the colony after 4 days is 6553 mosquitoes
2) After
Step-by-step explanation:
To answer this question you must use the growth formula
![N = N_0e ^ {kt}](https://tex.z-dn.net/?f=N%20%3D%20N_0e%20%5E%20%7Bkt%7D)
Where
is the initial population of mosquitoes = 1000
t is the time in days
k is the growth rate
N is the population according to the number of days
We know that when t = 1 and
then N = 1600
Then we use these values to find k.
![1600 = 1000e ^{k(1)}\\\\\frac{1600}{1000} = e ^ k\\\\ln(\frac{1600}{1000}) = k\\\\k = 0.47](https://tex.z-dn.net/?f=1600%20%3D%201000e%20%5E%7Bk%281%29%7D%5C%5C%5C%5C%5Cfrac%7B1600%7D%7B1000%7D%20%3D%20e%20%5E%20k%5C%5C%5C%5Cln%28%5Cfrac%7B1600%7D%7B1000%7D%29%20%3D%20k%5C%5C%5C%5Ck%20%3D%200.47)
Now that we know k we can find the size of the colony after 4 days.
![N = 1000e ^ {0.47(4)}\\\\N = 6553\ mosquitoes](https://tex.z-dn.net/?f=N%20%3D%201000e%20%5E%20%7B0.47%284%29%7D%5C%5C%5C%5CN%20%3D%206553%5C%20mosquitoes)
To know how long it should take for the population to reach 10,000 mosquitoes we must do N = 10000 and solve for t.
![10000 = 1000e ^ {0.47t}\\\\10 = e ^ {0.47t}\\\\ln(10) = 0.47t\\\\t = \frac{ln(10)}{0.47}\\\\t = 4.9\ days](https://tex.z-dn.net/?f=10000%20%3D%201000e%20%5E%20%7B0.47t%7D%5C%5C%5C%5C10%20%3D%20e%20%5E%20%7B0.47t%7D%5C%5C%5C%5Cln%2810%29%20%3D%200.47t%5C%5C%5C%5Ct%20%3D%20%5Cfrac%7Bln%2810%29%7D%7B0.47%7D%5C%5C%5C%5Ct%20%3D%204.9%5C%20days)
Answer:
Volume is 21
Explanation
Base length is 4.5
Widgth is 3.5
and height is 4 (I can't tell if its 2 because picture is blurry)
V=lwh/3=4.5·3.5·4= 21
Answer: -216
Step-by-step explanation:
To solve the exercise you must use the formula shown below:
![Sn=\frac{(a_1+a_n)n}{2}](https://tex.z-dn.net/?f=Sn%3D%5Cfrac%7B%28a_1%2Ba_n%29n%7D%7B2%7D)
Where:
![a_1=152\\a_n=a_{24}](https://tex.z-dn.net/?f=a_1%3D152%5C%5Ca_n%3Da_%7B24%7D)
You should find ![a_{24}](https://tex.z-dn.net/?f=a_%7B24%7D)
The formula to find it is:
![a_n=a_1+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d)
Where d is the difference between two consecutive terms.
![d=138-152=-14](https://tex.z-dn.net/?f=d%3D138-152%3D-14)
Then:
![a_{24}=152+(24-1)(14)=-170](https://tex.z-dn.net/?f=a_%7B24%7D%3D152%2B%2824-1%29%2814%29%3D-170)
Substitute it into the first formula. Therefore, you obtain:
![S_{24}=\frac{(152-170)(24)}{2}=-216](https://tex.z-dn.net/?f=S_%7B24%7D%3D%5Cfrac%7B%28152-170%29%2824%29%7D%7B2%7D%3D-216)
Answer:
Step-by-step explanation:
4^-3
=1/4^3
=1/64
Answer:
The answer to your question is: letter D
Step-by-step explanation:
First we need to find the distances between the points,
distance AB = 8 get it just by counting the points in the graph
distance AC = 9 get it just by counting the points in the graph
To know the distance BC, use the pythagorean theorem
c2 = a2 +b2
c2 = 8² + 9²
c² = 64 + 81
c² = 145
c = 12.04
Finally, perimeter = AB + AC + BC
= 8 + 9 + 12.04
= 29.04 units