Answer:
The population will become 840 million in 2019.
Step-by-step explanation:
Given:
The exponential model of population is given as:
![A=682.2e^{0.013t}](https://tex.z-dn.net/?f=A%3D682.2e%5E%7B0.013t%7D)
Here, 't' is in years measured since 2003.
This means for the year 2003, t = 0 and so on.
Now, in order to get the year when the population is 840 million, we need to plug in 840 for 'A' and solve for 't'. Therefore,
![840=682.2e^{0.013t}\\\\e^{0.013t}=\frac{840}{682.2}\\\\e^{0.013t}=1.2313](https://tex.z-dn.net/?f=840%3D682.2e%5E%7B0.013t%7D%5C%5C%5C%5Ce%5E%7B0.013t%7D%3D%5Cfrac%7B840%7D%7B682.2%7D%5C%5C%5C%5Ce%5E%7B0.013t%7D%3D1.2313)
Taking natural log on both sides, we get:
![0.013t=\ln(1.2313)\\\\0.013t=0.2081\\\\t=\frac{0.2081}{0.013}\\\\t=16\ years](https://tex.z-dn.net/?f=0.013t%3D%5Cln%281.2313%29%5C%5C%5C%5C0.013t%3D0.2081%5C%5C%5C%5Ct%3D%5Cfrac%7B0.2081%7D%7B0.013%7D%5C%5C%5C%5Ct%3D16%5C%20years)
Therefore, 16 years after 2003, the population will be 840 million.
So, the year is equal to 2003 + 16 = 2019.
Hence, in the year 2019, the population will become 840 million.