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 street 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 street hockey programs in x years?

The function is :  

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  

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, the number of participants in the town's soccer program after years will be.....

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

Thus, the number of participants in the town's street hockey program after years will be.....

If the total number of children participating in the two programs is represented as , then.....

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:  

step-by-step explanation:

a child is 12 years old, and his father is 32 years older. in how many years will the age of the father be 2 times the age of the child?

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this needs to be the answer format, or else your answer is incomplete.

if the number of years is x, then the equation is

in __ years

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: