Answer:
It will take the 20 years for the population to quadruple.
Step-by-step explanation:
Exponential population growth:
An exponential model for population growth has the following model:
![P(t) = P(0)(1+r)^t](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281%2Br%29%5Et)
In which P(0) is the initial population and r is the growth rate, as a decimal.
It grows with a doubling time of 10 years.
This means that
. We use this to find r. So
![P(t) = P(0)(1+r)^t](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281%2Br%29%5Et)
![2P(0) = P(0)(1+r)^10](https://tex.z-dn.net/?f=2P%280%29%20%3D%20P%280%29%281%2Br%29%5E10)
![(1+r)^10 = 2](https://tex.z-dn.net/?f=%281%2Br%29%5E10%20%3D%202)
![\sqrt[10]{(1+r)^10} = \sqrt[10]{2}](https://tex.z-dn.net/?f=%5Csqrt%5B10%5D%7B%281%2Br%29%5E10%7D%20%3D%20%5Csqrt%5B10%5D%7B2%7D)
![1+r = 2^{\frac{1}{10}}](https://tex.z-dn.net/?f=1%2Br%20%3D%202%5E%7B%5Cfrac%7B1%7D%7B10%7D%7D)
![1 + r = 1.0718](https://tex.z-dn.net/?f=1%20%2B%20r%20%3D%201.0718)
So
![P(t) = P(0)(1+r)^t](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281%2Br%29%5Et)
![P(t) = P(0)(1.0718)^t](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281.0718%29%5Et)
Determine how long it will take for the population to quadruple.
This is t for which P(t) = 4P(0). So
![P(t) = P(0)(1.0718)^t](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281.0718%29%5Et)
![4P(0) = P(0)(1.0718)^t](https://tex.z-dn.net/?f=4P%280%29%20%3D%20P%280%29%281.0718%29%5Et)
![(1.0718)^t = 4](https://tex.z-dn.net/?f=%281.0718%29%5Et%20%3D%204)
![\log{(1.0718)^t} = \log{4}](https://tex.z-dn.net/?f=%5Clog%7B%281.0718%29%5Et%7D%20%3D%20%5Clog%7B4%7D)
![t\log{1.0718} = \log{4}](https://tex.z-dn.net/?f=t%5Clog%7B1.0718%7D%20%3D%20%5Clog%7B4%7D)
![t = \frac{\log{4}}{\log{1.0718}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Clog%7B4%7D%7D%7B%5Clog%7B1.0718%7D%7D)
![t = 20](https://tex.z-dn.net/?f=t%20%3D%2020)
It will take the 20 years for the population to quadruple.
The maximum is 4 days
200:42= 4,76
Answer:
The increasing interval is ![S=(-2,\infty)](https://tex.z-dn.net/?f=S%3D%28-2%2C%5Cinfty%29)
Step-by-step explanation:
This absolute function has a vertex in x=-2. Now, from this point, the function has a positive slope (increasing), which means for values of x equals to -1,0,1,2,3,...,n.
Therefore the interval will
![S=(-2,\infty)](https://tex.z-dn.net/?f=S%3D%28-2%2C%5Cinfty%29)
I hope it helps you!
Answer:
y = 28
Step-by-step explanation:
since this is an Isosceles triangle (x - 5)° must be equal to 34°
x - 5 = 34
x = 39
the sum of interior angles in a triangle is equal to 180°
if the two angles 34 + 34 = 68
Then the third angle is 180 - 68 = 112°
4y = 112
y = 28