Answer:
the base is 10 and the height is 6.4
A).(x - 10) X (x - 4)
(4 - 10) X (4 - 4)
6 X 0 = 0
Answer:
Step-by-step explanation:
First, organize all of the like terms. All of the numbers to one side, all of the variables to the other. Then, divide to get x by itself.
Answer:
(a)![N(t)=Noe^{kt}](https://tex.z-dn.net/?f=N%28t%29%3DNoe%5E%7Bkt%7D)
(b)5,832 Mosquitoes
(c)5 days
Step-by-step explanation:
(a)Given an original amount
at t=0. The population of the colony with a growth rate
, where k is a constant is given as:
![N(t)=Noe^{kt}](https://tex.z-dn.net/?f=N%28t%29%3DNoe%5E%7Bkt%7D)
(b)If
and the population after 1 day, N(1)=1800
Then, from our model:
N(1)=1800
![1800=1000e^{k}\\$Divide both sides by 1000\\e^{k}=1.8\\$Take the natural logarithm of both sides\\k=ln(1.8)](https://tex.z-dn.net/?f=1800%3D1000e%5E%7Bk%7D%5C%5C%24Divide%20both%20sides%20by%201000%5C%5Ce%5E%7Bk%7D%3D1.8%5C%5C%24Take%20the%20natural%20logarithm%20of%20both%20sides%5C%5Ck%3Dln%281.8%29)
Therefore, our model is:
![N(t)=1000e^{t*ln(1.8)}\\N(t)=1000\cdot1.8^t](https://tex.z-dn.net/?f=N%28t%29%3D1000e%5E%7Bt%2Aln%281.8%29%7D%5C%5CN%28t%29%3D1000%5Ccdot1.8%5Et)
In 3 days time
![N(3)=1000\cdot1.8^3=5832](https://tex.z-dn.net/?f=N%283%29%3D1000%5Ccdot1.8%5E3%3D5832)
The population of mosquitoes in 3 days time will be approximately 5832.
(c)If the population N(t)=20,000,we want to determine how many days it takes to attain that value.
From our model
![N(t)=1000\cdot1.8^t\\20000=1000\cdot1.8^t\\$Divide both sides by 1000\\20=1.8^t\\$Convert to logarithm form\\Log_{1.8}20=t\\\frac{Log 20}{Log 1.8}=t\\ t=5.097\approx 5\; days](https://tex.z-dn.net/?f=N%28t%29%3D1000%5Ccdot1.8%5Et%5C%5C20000%3D1000%5Ccdot1.8%5Et%5C%5C%24Divide%20both%20sides%20by%201000%5C%5C20%3D1.8%5Et%5C%5C%24Convert%20to%20logarithm%20form%5C%5CLog_%7B1.8%7D20%3Dt%5C%5C%5Cfrac%7BLog%2020%7D%7BLog%201.8%7D%3Dt%5C%5C%20t%3D5.097%5Capprox%205%5C%3B%20days)
In approximately 5 days, the population of mosquitoes will be 20,000.