Answer:
<em>The function is :
</em>
Step-by-step explanation:
Suppose, after
years, the number of participants in the town's soccer program is
and in the town's street hockey program is ![y_{2}](https://tex.z-dn.net/?f=y_%7B2%7D)
This year, there are 120 children participating in each program.
The number of participants in the town's soccer program increases by 10% each year.
Using the exponential growth formula, <u>the number of participants in the town's soccer program after
years will be</u>.....
![y_{1}=120(1+0.10)^x\\ \\ y_{1}=120(1.10)^x](https://tex.z-dn.net/?f=y_%7B1%7D%3D120%281%2B0.10%29%5Ex%5C%5C%20%5C%5C%20y_%7B1%7D%3D120%281.10%29%5Ex)
The number of participants in the town's street hockey program increases by 10 children each year.
So, the number of increased participants in
years ![=10x](https://tex.z-dn.net/?f=%3D10x)
Thus, <u>the number of participants in the town's street hockey program after
years will be</u>.....
![y_{2}=120+10x](https://tex.z-dn.net/?f=y_%7B2%7D%3D120%2B10x)
If the total number of children participating in the two programs is represented as
, then.....
![y= y_{1}+y_{2}\\ \\ y=120(1.10)^x+120+10x](https://tex.z-dn.net/?f=y%3D%20y_%7B1%7D%2By_%7B2%7D%5C%5C%20%5C%5C%20y%3D120%281.10%29%5Ex%2B120%2B10x)
So, the function that can be used to predict the total number of children participating in the town's soccer and street hockey programs in x years will be: ![y=120(1.10)^x+120+10x](https://tex.z-dn.net/?f=y%3D120%281.10%29%5Ex%2B120%2B10x)