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.