Final answer:
The initial deposit X needed to reach a total amount of $350 at t=4, after a subsequent deposit of $100 at t=3, with no interest applied, is $250.
Step-by-step explanation:
The student is asking a question related to simple interest in the context of mathematics, specifically a problem involving initial and subsequent deposits into an account and finding an unknown deposit. Let's find the value of the initial deposit, X, given the following conditions:
- A deposit of X dollars is made at t=0.
- A deposit of $100 is made at t=3.
- The total amount in the account at t=4 is $350.
As there is no mention of interest being applied to the deposits, we will assume that the account does not earn interest over time. Therefore, the problem simplifies to an equation where X plus the second deposit ($100) equals the total amount after 4 years ($350).
The equation representing the final amount is:
X + $100 = $350
To find the value of X, we simply subtract $100 from both sides of the equation:
X = $350 - $100
X = $250
The initial deposit, X, required to reach a total of $350 at t=4 after making a subsequent deposit of $100 at t=3 is $250.