A person has 415 dollars in a cookie jar. Every month they add 30 additional dollars to the jar. The linear function that models this situation is $$ S(x)= $$ where $$ x $$ represents Select an answerv and $$ S(x) $$ represents Select an answerv. How much money will be in the jar after 12 months? dollars How long will it take to save $$ \$ 1075 $$ ? months

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UpStudy AI · Accepted Answer

We model the situation with the linear function

$$
S(x)=415+30x
$$

where $$ x $$ represents the number of months and $$ S(x) $$ represents the total amount of money in the cookie jar (in dollars).

### Step 1. Money in the Jar After 12 Months

Substitute $$ x=12 $$ into the function:

$$
S(12)=415+30(12)
$$

Calculate $$ 30(12)=360 $$:

$$
S(12)=415+360=775
$$

After 12 months, there will be $$ \boxed{775} $$ dollars in the jar.

### Step 2. Time Required to Save $$\$1075$$

Set the equation $$ S(x)=1075 $$:

$$
415+30x=1075
$$

Subtract 415 from both sides:

$$
30x=1075-415=660
$$

Divide both sides by 30:

$$
x=\frac{660}{30}=22
$$

It will take $$ \boxed{22} $$ months to save $$\$1075$$.
The linear function is $$ S(x) = 415 + 30x $$, where $$ x $$ is the number of months and $$ S(x) $$ is the total money in the jar. After 12 months, there will be \$775 in the jar. It will take 22 months to save \$1075.

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