ANSWER
![\text{9 years}](https://tex.z-dn.net/?f=%5Ctext%7B9%20years%7D)
EXPLANATION
We want to find the number of years that it will take the population to double.
To do this, we have to apply the exponential growth function:
![y=a(1+r)^t](https://tex.z-dn.net/?f=y%3Da%281%2Br%29%5Et)
where y = final value
a = initial value
r = rate of growth
t = time (in years)
For the population to double, it means that the final value must be 2 times the initial value:
![y=2a](https://tex.z-dn.net/?f=y%3D2a)
Substitute the given values into the function above:
![\begin{gathered} 2a=a(1+\frac{8}{100})^t \\ \frac{2a}{a}=(1+0.08)^t=1.08^t \\ 2=1.08^t \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%202a%3Da%281%2B%5Cfrac%7B8%7D%7B100%7D%29%5Et%20%5C%5C%20%5Cfrac%7B2a%7D%7Ba%7D%3D%281%2B0.08%29%5Et%3D1.08%5Et%20%5C%5C%202%3D1.08%5Et%20%5Cend%7Bgathered%7D)
To solve further, convert the function from an exponential function to a logarithmic function as follows:
![\log _{1.08}2=t](https://tex.z-dn.net/?f=%5Clog%20_%7B1.08%7D2%3Dt)
Solve for t:
![\begin{gathered} \frac{\log _{10}2}{\log _{10}1.08}=t \\ \Rightarrow t=9\text{ years} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B%5Clog%20_%7B10%7D2%7D%7B%5Clog%20_%7B10%7D1.08%7D%3Dt%20%5C%5C%20%5CRightarrow%20t%3D9%5Ctext%7B%20years%7D%20%5Cend%7Bgathered%7D)
It will take 9 years for the population to double.
Answer:
![F(4) = \frac {1}{256}](https://tex.z-dn.net/?f=%20F%284%29%20%3D%20%5Cfrac%20%7B1%7D%7B256%7D%20)
Step-by-step explanation:
Given the following mathematical function;
![F(x) = \frac {1}{4^{x}}](https://tex.z-dn.net/?f=%20F%28x%29%20%3D%20%5Cfrac%20%7B1%7D%7B4%5E%7Bx%7D%7D%20)
<u>When x = 1</u>
![F(1) = \frac {1}{4^{1}}](https://tex.z-dn.net/?f=%20F%281%29%20%3D%20%5Cfrac%20%7B1%7D%7B4%5E%7B1%7D%7D%20)
![F(1) = \frac {1}{4}](https://tex.z-dn.net/?f=%20F%281%29%20%3D%20%5Cfrac%20%7B1%7D%7B4%7D%20)
<u>When x = 2</u>
![F(2) = \frac {1}{4^{2}}](https://tex.z-dn.net/?f=%20F%282%29%20%3D%20%5Cfrac%20%7B1%7D%7B4%5E%7B2%7D%7D%20)
![F(2) = \frac {1}{4*4}](https://tex.z-dn.net/?f=%20F%282%29%20%3D%20%5Cfrac%20%7B1%7D%7B4%2A4%7D%20)
![F(2) = \frac {1}{16}](https://tex.z-dn.net/?f=%20F%282%29%20%3D%20%5Cfrac%20%7B1%7D%7B16%7D%20)
<u>When x = 3</u>
![F(3) = \frac {1}{4^{3}}](https://tex.z-dn.net/?f=%20F%283%29%20%3D%20%5Cfrac%20%7B1%7D%7B4%5E%7B3%7D%7D%20)
![F(3) = \frac {1}{4*4*4}](https://tex.z-dn.net/?f=%20F%283%29%20%3D%20%5Cfrac%20%7B1%7D%7B4%2A4%2A4%7D%20)
![F(3) = \frac {1}{4*4*4}](https://tex.z-dn.net/?f=%20F%283%29%20%3D%20%5Cfrac%20%7B1%7D%7B4%2A4%2A4%7D%20)
<u>When x = 4</u>
![F(4) = \frac {1}{4^{4}}](https://tex.z-dn.net/?f=%20F%284%29%20%3D%20%5Cfrac%20%7B1%7D%7B4%5E%7B4%7D%7D%20)
![F(4) = \frac {1}{4*4*4*4}](https://tex.z-dn.net/?f=%20F%284%29%20%3D%20%5Cfrac%20%7B1%7D%7B4%2A4%2A4%2A4%7D%20)
![F(4) = \frac {1}{256}](https://tex.z-dn.net/?f=%20F%284%29%20%3D%20%5Cfrac%20%7B1%7D%7B256%7D%20)
<u>When x = 5</u>
![F(5) = \frac {1}{4^{5}}](https://tex.z-dn.net/?f=%20F%285%29%20%3D%20%5Cfrac%20%7B1%7D%7B4%5E%7B5%7D%7D%20)
![F(5) = \frac {1}{4*4*4*4*4}](https://tex.z-dn.net/?f=%20F%285%29%20%3D%20%5Cfrac%20%7B1%7D%7B4%2A4%2A4%2A4%2A4%7D%20)
![F(5) = \frac {1}{1024}](https://tex.z-dn.net/?f=%20F%285%29%20%3D%20%5Cfrac%20%7B1%7D%7B1024%7D%20)
Answer:
2 over 9 can be expressed as a repeating decimal.
Step-by-step explanation:
I got 2(15+N) I hope this helped you
Answer:
The probability that a point is in the shaded area would be 0.75
Step-by-step explanation:
Again, we must find the area of each square to find our answer.
The smaller square has a side length of 5 so we can find the area by squaring that value
![5^{2} =25](https://tex.z-dn.net/?f=5%5E%7B2%7D%20%3D25)
The larger square has a side length of 10 so we can find the area by squaring that value
![10^{2} =100](https://tex.z-dn.net/?f=10%5E%7B2%7D%20%3D100)
As we are looking for the shaded value, we must subtract the white portion from the total area
This would mean that
100 - 25 = 75
We can then write the ratio of the shaded area to the total area which would be
![\frac{75}{100}](https://tex.z-dn.net/?f=%5Cfrac%7B75%7D%7B100%7D)
As a decimal this would be
0.75