Answer:
<em>The Estimate for the population in 2008 is 33 million </em>
Step-by-step explanation:
<u>Exponential Function</u>
Some real-life situations can be modeled by using the exponential function which takes the form
![P = Ae^{kt}](https://tex.z-dn.net/?f=P%20%3D%20Ae%5E%7Bkt%7D)
Where A and k are constants, and t is the independent variable.
We are given two data. A country's population in 1992 was 28 million and in 1999 it was 30 million.
Let's express P as the population in million and t the time in years elapsed since 1992.
The information can be written as two points: (0,28), (7,30). Please recall that the second data comes from the year 1999, seven years after the zero reference.
We only have to replace both points in the general form:
![28 = Ae^{k(0)}=A(1)=A](https://tex.z-dn.net/?f=28%20%3D%20Ae%5E%7Bk%280%29%7D%3DA%281%29%3DA)
We know A=28 million
Also
![30 = 28e^{k{(7)}}](https://tex.z-dn.net/?f=30%20%3D%2028e%5E%7Bk%7B%287%29%7D%7D)
![28e^{7k}=30](https://tex.z-dn.net/?f=28e%5E%7B7k%7D%3D30)
![\displaystyle e^{7k}=\frac{30}{28}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20e%5E%7B7k%7D%3D%5Cfrac%7B30%7D%7B28%7D)
Taking logarithms
![\displaystyle 7k=ln\left ( \frac{30}{28} \right )](https://tex.z-dn.net/?f=%5Cdisplaystyle%207k%3Dln%5Cleft%20%28%20%5Cfrac%7B30%7D%7B28%7D%20%5Cright%20%29)
Solving for k
![\displaystyle k=\frac{ln\left ( \frac{30}{28} \right )}{7}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20k%3D%5Cfrac%7Bln%5Cleft%20%28%20%5Cfrac%7B30%7D%7B28%7D%20%5Cright%20%29%7D%7B7%7D)
![k=0.00986](https://tex.z-dn.net/?f=k%3D0.00986)
The model is complete now:
![P = 28e^{0.00986t}](https://tex.z-dn.net/?f=P%20%3D%2028e%5E%7B0.00986t%7D)
For the year 2008, t=2008-1992=16 years
![P = 28e^{0.00986(16)}](https://tex.z-dn.net/?f=P%20%3D%2028e%5E%7B0.00986%2816%29%7D)
![P = 28(1.1708)](https://tex.z-dn.net/?f=P%20%3D%2028%281.1708%29)
![P=32.78\ \approx 33](https://tex.z-dn.net/?f=P%3D32.78%5C%20%5Capprox%2033)
The Estimate for the population in 2008 is 33 million
Answer:
![\huge\boxed{m = \frac{y-b}{x}}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7Bm%20%3D%20%5Cfrac%7By-b%7D%7Bx%7D%7D)
Step-by-step explanation:
In order to solve for
and we want to solve for
, we want to get m on one side of the equation.
![y = mx+b](https://tex.z-dn.net/?f=y%20%3D%20mx%2Bb)
Let’s subtract b from both sides.
![y - b = mx](https://tex.z-dn.net/?f=y%20-%20b%20%3D%20mx)
Now we can divide both sides by x so we have m on one side of the equation.
![\frac{y-b}{x} = m](https://tex.z-dn.net/?f=%5Cfrac%7By-b%7D%7Bx%7D%20%3D%20m)
Hope this helped!
Answer:
Tuba Girl
Step-by-step explanation:
Its obviuous
Answer: 1967
Step-by-step explanation:
Ada was 15 years when her sister Ngozi was 18 years.
This means that Ngozi is older than Ada by:
= 18 - 15
= 3 years
If Ngozi is older by 3 years, this means that she must have been born 3 years earlier than Ada
If Ada was born in 1970, Ngozi was born:
= 1970 - 3
= 1967