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The Rock Rollers released their first album, Metamorphic, when they were still mostly unknown, and the value of the album initially declined. As the band became more famous and the album became more popular, its value started to increase. The value of the album in dollars can be modeled by the expression 0.2t2−4t+250.2t^2-4t+25, where tt is the time in years after it was first released. What does the number 2525 represent in the expression?

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Q. The Rock Rollers released their first album, Metamorphic, when they were still mostly unknown, and the value of the album initially declined. As the band became more famous and the album became more popular, its value started to increase. The value of the album in dollars can be modeled by the expression 0.2t2−4t+250.2t^2-4t+25, where tt is the time in years after it was first released. What does the number 2525 represent in the expression?
  1. Analyze the expression: Analyze the expression for the album's value.\newlineThe value of the album is given by the expression 0.2t2−4t+250.2t^2 - 4t + 25, where tt is the time in years after the album was first released.\newlineThe expression is a quadratic equation, which typically models a parabolic change in value over time.
  2. Identify constant term: Identify the constant term in the expression.\newlineIn the given quadratic expression, the constant term is 2525.\newlineThe constant term in a quadratic equation represents the initial value of the function when the variable (in this case, tt) is zero.
  3. Interpret constant term: Interpret the constant term in the context of the problem.\newlineSince tt represents the time in years after the album was first released, when t=0t = 0, it corresponds to the time of the album's release.\newlineTherefore, the constant term 2525 represents the initial value of the album in dollars at the time of its release.

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