3 1/6 = 19/6
2 1/9 = 19/9
19/6 / 19/9 = 19*9/19*6 = 9/6 = 3/2
Answer:
Step-by-step explanation:
I think it is A
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.
<h2>
The stone fall in air for 7 seconds and fall in water for 5 seconds.</h2>
Step-by-step explanation:
Total distance to sea bed = 127 m
Let the distance traveled in air be s.
Distance traveled in water = 127 - s
Average velocity in air = 16 m/s
Average velocity in water = 3 m/s
Distance traveled in air = Average velocity in air x Time in air
s = 16 x t₁
![t_1=\frac{s}{16}](https://tex.z-dn.net/?f=t_1%3D%5Cfrac%7Bs%7D%7B16%7D)
Distance traveled in water = Average velocity in water x Time in water
127-s = 3 x t₂
![t_2=\frac{127-s}{3}](https://tex.z-dn.net/?f=t_2%3D%5Cfrac%7B127-s%7D%7B3%7D)
We have total time is 12 seconds
That is
t₁ + t₂ = 12
![\frac{s}{16}+\frac{127-s}{3}=12\\\\3s+2032-16s=576\\\\13s=1456\\\\s=112m](https://tex.z-dn.net/?f=%5Cfrac%7Bs%7D%7B16%7D%2B%5Cfrac%7B127-s%7D%7B3%7D%3D12%5C%5C%5C%5C3s%2B2032-16s%3D576%5C%5C%5C%5C13s%3D1456%5C%5C%5C%5Cs%3D112m)
We have
s = 16 x t₁
112 = 16 x t₁
t₁ = 7 s
t₁ + t₂ = 12
7 + t₂ = 12
t₂ = 5 s
The stone fall in air for 7 seconds and fall in water for 5 seconds.