Answer:
The predicted number of customers for APP in 2022 is of 1.37 million, and of BPP is of 2.59 million.
Step-by-step explanation:
Exponential function:
An exponential function has the following format:
![y(t) = y(0)r^t](https://tex.z-dn.net/?f=y%28t%29%20%3D%20y%280%29r%5Et)
In which
is the initial value and r is the rate of change.
11% of a city's population switches from phone service provider APP to phone service provider BPP each year, and about 5% of the populaton switches from BPP to APP each year.
This means that each year, the BPP amount increases by 11 - 5 = 6%, and the APP decreases by 6%. So the equations are:
BPP:
![B(t) = B(0)(1 + 0.06)^t](https://tex.z-dn.net/?f=B%28t%29%20%3D%20B%280%29%281%20%2B%200.06%29%5Et)
![B(t) = B(0)(1.06)^t](https://tex.z-dn.net/?f=B%28t%29%20%3D%20B%280%29%281.06%29%5Et)
APP:
![A(t) = A(0)(1 - 0.06)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281%20-%200.06%29%5Et)
![A(t) = A(0)(0.94)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%280.94%29%5Et)
In 2018, there were 1.75 million customers of APP and 2.05 million customers of BPP.
This means that ![A(0) = 1.75, B(0) = 2.05](https://tex.z-dn.net/?f=A%280%29%20%3D%201.75%2C%20B%280%29%20%3D%202.05)
Thus
![B(t) = 2.05(1.06)^t](https://tex.z-dn.net/?f=B%28t%29%20%3D%202.05%281.06%29%5Et)
![A(t) = 1.75(0.94)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%201.75%280.94%29%5Et)
Find the predicted number of customers for each provider in 2022.
2022 - 2018 = 4, so we have to find A(4) and B(4).
![B(4) = 2.05(1.06)^4 = 2.59](https://tex.z-dn.net/?f=B%284%29%20%3D%202.05%281.06%29%5E4%20%3D%202.59)
![A(4) = 1.75(0.94)^4 = 1.37](https://tex.z-dn.net/?f=A%284%29%20%3D%201.75%280.94%29%5E4%20%3D%201.37)
The predicted number of customers for APP in 2022 is of 1.37 million, and of BPP is of 2.59 million.