Question

The director of the town's sports programs is studying trends in enrollment over time. She finds that the number of participants in the town's soccer program increases by 10% each year, and the number of participants in the town's inline hockey program increases by 10 children each year. This year, there are 120 children participating in each program. Which function can be used to predict the total number of children participating in the town's soccer and inline hockey programs in x years?

Answer 1

Answer:

The required function is:  $A=120(1.1)^{x}+10x+120$

Step-by-step explanation:

Given:

i)This year, there are 120 children participating in each program.

ii) The no. of participants in the soccer program increases 10% every year

iii)The n0 of participants in the inline hockey program increased by 10 children every year.

Solution:

Let, after x years the no. of participants in the soccer program is $a_{1}$ and the no. of participants in the inline hockey program is $a_{2}$

∴ Using Exponential Growth Formula, the no. of participants in the soccer program after b years will be:

$a_{1}=120(1+\frac{10}{100}) ^{x}$

⇒$a_{1}=120(1+0.1) ^{x}$

⇒$a_{1}=120(1.1) ^{x}$

and, the no. of increased participants in the inline hockey after x years = $10x$

∴The no. of participants in the inline hockey after x years:

$a_{2}=120+10x$

Now,

If the total no. of children participating in the two programs is represent as: $A$

Then,

$A=a_{1}+a_{2}$

⇒ $A=120(1.1)^{x}+10x+120$

∴ The required function that can predict the no. of children participating in the town's soccer and inline hockey programs in x years is:

$A=120(1.1)^{x}+10x+120$

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