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:

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



![\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)


So


Determine how long it will take for the population to quadruple.
This is t for which P(t) = 4P(0). So







It will take the 20 years for the population to quadruple.
Answer:
B) 24/35
Step-by-step explanation:
Cos(X)= Adjacent/Hypotenuse
Cos(X) = 24/25
Therefore, option B is your answer.
Hope this answers your question!!
Answer:
x = 8
Step-by-step explanation:
well using the theorem we have
![\frac{6}{9}=\frac{x}{12}\\\\\frac{2}{3}=\frac{x}{12}\\\\12[\frac{2}{3}]=12[\frac{x}{12}]\\\\4\cdot 2=x\\\\x=8](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B9%7D%3D%5Cfrac%7Bx%7D%7B12%7D%5C%5C%5C%5C%5Cfrac%7B2%7D%7B3%7D%3D%5Cfrac%7Bx%7D%7B12%7D%5C%5C%5C%5C12%5B%5Cfrac%7B2%7D%7B3%7D%5D%3D12%5B%5Cfrac%7Bx%7D%7B12%7D%5D%5C%5C%5C%5C4%5Ccdot%202%3Dx%5C%5C%5C%5Cx%3D8)
-2(x - 5) + 4(9 + x)
-2x + 10 + 36 + 4x
=2x + 46