
Jason decides to open a savings account to save money for a new apple watch. He makes an initial deposit of $45 and plans to deposit $20 per week from his part-time job.

Write the linear function f(t) to represent the total amount of money in Jason's account after t weeks.

To find the linear function representing the total amount of money in Jason's account after $ t $ weeks, we need to consider both his initial deposit and his weekly deposits.

### Step-by-step construction of the linear function:

1. **Initial Deposit**: Jason starts with an initial deposit of $45. This is a one-time amount added to the account when he opens it.

2. **Weekly Deposit**: Jason deposits $20 every week. The amount of money added to the account each week depends on the number of weeks $ t $.

### Formulating the Linear Function:

The total amount of money $ f(t) $ in Jason's account after $ t $ weeks can be represented as:

\[
f(t) = \text{initial deposit} + (\text{weekly deposit} \times \text{number of weeks})
\]

Substitute the values:

\[
f(t) = 45 + 20t
\]

### Final Linear Function:

The linear function $ f(t) $ that represents the total amount of money in Jason's account after $ t $ weeks is:

\[
f(t) = 45 + 20t
\]

This function indicates that for every week that passes, an additional $20 is added to the initial $45.

Would you like to see more details or have any questions about this solution?

Here are some related questions you might find interesting:
1. How much money will Jason have in his account after 10 weeks?
2. If Jason wants to save up for an Apple Watch that costs $399, how many weeks will it take?
3. What is the rate of change of Jason's savings per week?
4. How much money will Jason have saved after 0 weeks?
5. What happens to Jason’s savings if he increases his weekly deposit to $30?

**Tip:** Remember, linear functions like this one have a constant rate of change, which is the amount added or subtracted in each time period.

Discover how to calculate the growth of Jason's savings using a linear function. This problem involves his initial deposit of $45 and weekly deposits of $20 from his part-time job. Learn step-by-step how to formulate and apply the linear function to determine his savings over time. Suitable for Grades 7-9.

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