Final answer:
The question is about solving an initial value problem and a separate task of solving a quadratic equation using the quadratic formula. The quadratic equation in the question is t² + 10t - 2000 = 0, which can be solved using the values a = 1, b = 10, c = -2000 in the quadratic formula.
Step-by-step explanation:
The student's question involves solving an initial value problem and employing the quadratic formula to solve a quadratic equation. The initial value problem provided is a first-order linear differential equation. However, the question does not provide a specific initial condition, which would be necessary to find a particular solution to the differential equation. Instead, the question seems to mix two different mathematical problems. We can address the part of the question that involves the quadratic equation t² + 10t - 2000 = 0, which is a common type of problem in high school mathematics.
To solve the quadratic equation using the quadratic formula, you first confirm that the equation is in the standard form at² + bt + c = 0, in this case, with a = 1, b = 10, and c = -2000. The quadratic formula is given by t = (-b ± √(b² - 4ac)) / (2a). Plugging the values into the formula gives the solutions for t.