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 $0.2t^2 - 4t + 25$ , where $t$ is the time in years after it was first released. $\newline$ What does the number $25$ represent in the expression? $\newline$ Choices: $\newline$ (A)the time in years from when the album was released until its value was the same as when it was first released $\newline$ (B)the time in years from when the album was released until its value was the least $\newline$ (C)the album's value in dollars when it was worth the least $\newline$ (D)the album's value in dollars when it was first released

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Algebra 1

Interpret parts of quadratic expressions: word problems

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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

0.2t^2 - 4t + 25

, where

t

is the time in years after it was first released.

\newline

What does the number

25

represent in the expression?

\newline

Choices:

\newline

(A)the time in years from when the album was released until its value was the same as when it was first released

\newline

(B)the time in years from when the album was released until its value was the least

\newline

(C)the album's value in dollars when it was worth the least

\newline

(D)the album's value in dollars when it was first released

Identify Constant Term Meaning: The expression for the value of the album is $0.2t^2 - 4t + 25$ . We need to identify the meaning of the constant term, which is $25$ .
Understand Initial Value: The constant term in a quadratic equation represents the initial value before any changes occur. In this context, it means the value of the album when it was first released, before time started to pass (when $t=0$ ).
Confirm Initial Value: Plug in $t=0$ into the expression to confirm that $25$ is the initial value. $\newline$ $0.2(0)^2 - 4(0) + 25 = 25$ .