Questions: A popular streaming show ends with contestants doing one final task that is worth 10,000. The task is very difficult to complete, for each week that it goes unfinished, the show adds 500 to the jackpot. Assuming no contestant is able to win the jackpot, complete the model that would calculate the total jackpot value for a number of weeks in the future.

A popular streaming show ends with contestants doing one final task that is worth 10,000. The task is very difficult to complete, for each week that it goes unfinished, the show adds 500 to the jackpot. Assuming no contestant is able to win the jackpot, complete the model that would calculate the total jackpot value for a number of weeks in the future.
Transcript text: A popular streaming show ends with contestants doing one final task that is worth $\$ 10,000$. The task is very difficult to complete, for each week that it goes unfinished, the show adds $\$ 500$ to the jackpot. Assuming no contestant is able to win the jackpot, complete the model that would calculate the total jackpot value for a number of weeks in the future.
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Solution

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Solution Steps

To calculate the total jackpot value after a certain number of weeks, we start with the initial jackpot amount and add the weekly increment for each week that passes. The initial jackpot is $10,000, and it increases by $500 each week. Therefore, the total jackpot after a given number of weeks can be calculated by adding $500 times the number of weeks to the initial amount.

Step 1: Define the Problem

We need to calculate the total jackpot value after a certain number of weeks, given that the initial jackpot is \$10,000 and it increases by \$500 each week.

Step 2: Establish the Formula

The total jackpot after \( n \) weeks can be expressed as: \[ \text{Total Jackpot} = 10000 + 500 \times n \] where \( n \) is the number of weeks.

Step 3: Calculate the Jackpot for 5 Weeks

Substitute \( n = 5 \) into the formula: \[ \text{Total Jackpot} = 10000 + 500 \times 5 \] \[ \text{Total Jackpot} = 10000 + 2500 \] \[ \text{Total Jackpot} = 12500 \]

Final Answer

The total jackpot after 5 weeks is \(\boxed{12500}\).

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