Answer:
Part 1 : ![I_A = 5.77 e^{0.01055t}](https://tex.z-dn.net/?f=I_A%20%3D%205.77%20e%5E%7B0.01055t%7D)
Part 2 : In 2069 the population would be 12 millions.
Step-by-step explanation:
Part 1 : Given function that shows the population( in millions ) of Israel after t years since 2000,
![I_A = A_0 e^{kt}](https://tex.z-dn.net/?f=I_A%20%3D%20A_0%20e%5E%7Bkt%7D)
If t = 0,
![I_A = 5.77](https://tex.z-dn.net/?f=I_A%20%3D%205.77)
![\implies 5.77 = A_0 e^{0}\implies A_0 = 5.77](https://tex.z-dn.net/?f=%5Cimplies%205.77%20%3D%20A_0%20e%5E%7B0%7D%5Cimplies%20A_0%20%3D%205.77)
If t = 77 years,
The population in 2077,
![I_A = A_0 e^{77k}=5.77 e^{77k}](https://tex.z-dn.net/?f=I_A%20%3D%20A_0%20e%5E%7B77k%7D%3D5.77%20e%5E%7B77k%7D)
According to the question,
Population in 2077 = 13 millions
![13 = 5.77 e^{77k}](https://tex.z-dn.net/?f=13%20%3D%205.77%20e%5E%7B77k%7D)
![\frac{13}{5.77} = e^{77k}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B5.77%7D%20%3D%20e%5E%7B77k%7D)
Taking ln both sides,
![\ln(\frac{13}{5.77}) = \ln(e^{77k})](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B13%7D%7B5.77%7D%29%20%3D%20%5Cln%28e%5E%7B77k%7D%29)
![\ln(\frac{13}{5.77}) = 77k](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B13%7D%7B5.77%7D%29%20%3D%2077k)
![\implies k = 0.010549\approx 0.01055](https://tex.z-dn.net/?f=%5Cimplies%20k%20%3D%200.010549%5Capprox%200.01055)
Hence, the required function would be,
![I_A = 5.77 e^{0.01055t}](https://tex.z-dn.net/?f=I_A%20%3D%205.77%20e%5E%7B0.01055t%7D)
Part 2 : If ![I_A = 12](https://tex.z-dn.net/?f=I_A%20%3D%2012)
![12 = 5.77 e^{0.01055t}](https://tex.z-dn.net/?f=12%20%3D%205.77%20e%5E%7B0.01055t%7D)
![\frac{12}{5.77} = e^{0.01055t}](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B5.77%7D%20%3D%20e%5E%7B0.01055t%7D)
Taking ln both sides,
![\ln(\frac{12}{5.77}) = \ln(e^{0.01055t})](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B12%7D%7B5.77%7D%29%20%3D%20%5Cln%28e%5E%7B0.01055t%7D%29)
![\ln(\frac{12}{5.77}) =0.01055t](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B12%7D%7B5.77%7D%29%20%3D0.01055t)
![\implies t\approx 69](https://tex.z-dn.net/?f=%5Cimplies%20t%5Capprox%2069)
∵ 2000 + 69 = 2069
Hence, in 2069 the population would be 12 millions.
The slope of the line that passes through points
is
![\dfrac{y_2-y_1}{x_2-x_1}.](https://tex.z-dn.net/?f=%20%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D.)
For the points (-4,-3) and (4,1) the slope is
![\dfrac{1-(-3)}{4-(-4)}=\dfrac{4}{8}=\dfrac{1}{2}.](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1-%28-3%29%7D%7B4-%28-4%29%7D%3D%5Cdfrac%7B4%7D%7B8%7D%3D%5Cdfrac%7B1%7D%7B2%7D.)
Two perpendicular lines have slopes that form product of -1, then the slope of perpendicular line is ![-\dfrac{1}{\frac{1}{2}}=-2.](https://tex.z-dn.net/?f=%20-%5Cdfrac%7B1%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D-2.)
The line that passes through the point (−4, 3) and has slope -2 has equation:
![y-3=-2(x+4),\\y=-2x-8+3,\\y=-2x-5.](https://tex.z-dn.net/?f=%20y-3%3D-2%28x%2B4%29%2C%5C%5Cy%3D-2x-8%2B3%2C%5C%5Cy%3D-2x-5.%20)
Answer: y=-2x-5.
Answer:
konichiwat
Step-by-step explanation:
Answer:
The measure of angle x is ![26.1\°](https://tex.z-dn.net/?f=26.1%5C%C2%B0)
Step-by-step explanation:
we know that
In the right triangle of the figure, the tangent of angle x is equal to divide the opposite side to angle x by the adjacent side to angle x
so
![tan(x)=\frac{26}{53}](https://tex.z-dn.net/?f=tan%28x%29%3D%5Cfrac%7B26%7D%7B53%7D)
![x=arctan(\frac{26}{53})=26.1\°](https://tex.z-dn.net/?f=x%3Darctan%28%5Cfrac%7B26%7D%7B53%7D%29%3D26.1%5C%C2%B0)
Hello there!
Answer:
![\boxed{D. x](https://tex.z-dn.net/?f=%5Cboxed%7BD.%20x%3C-3%7D)
Step-by-step explanation:
Distributive property: a(b+c)=ab+ac
First, you expand.
4(x-2)=4x-8
7x+1<4x-8
Subtract by 1 both sides of an equation.
7x+1-1<4x-8-1
Add/Subtract numbers from left/right.
8+1=9
7x<4x-9
Then, you subtract by 4x both sides of an equation.
7x-4x<4x-9-4x
Simplify equation.
3x<-9
Divide by 3 both sides of an equation.
3x/3<-9/3
Divide numbers from left/right.
-9/3=-3
<u><em>x<-3 is the final answer.</em></u>
Hope this helps!
Thanks!
-Charlie
Have a nice day! :)
:D