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The expression
5*1.15^(t) gives the area, in square meters, damaged by a fire as a function of minutes since the fire was discovered.
What does 5 represent in this expression?
Choose 1 answer:
(A) An area of 5 square meters had been damaged by the fire by the time it was discovered.
(B) It has been 5 minutes since the fire was discovered.
(C) The area damaged by the fire is multiplied by 5 each minute.

The expression $5 \cdot 1.15^{t}$ gives the area, in square meters, damaged by a fire as a function of minutes since the fire was discovered. $\newline$ What does $5$ represent in this expression? $\newline$ Choose $1$ answer: $\newline$ (A) An area of $5$ square meters had been damaged by the fire by the time it was discovered. $\newline$ (B) It has been $5$ minutes since the fire was discovered. $\newline$ (C) The area damaged by the fire is multiplied by $5$ each minute.

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Write exponential functions: word problems

Full solution

Q. The expression

5 \cdot 1.15^{t}

gives the area, in square meters, damaged by a fire as a function of minutes since the fire was discovered.

\newline

What does

5

represent in this expression?

\newline

Choose

1

answer:

\newline

(A) An area of

5

square meters had been damaged by the fire by the time it was discovered.

\newline

(B) It has been

5

minutes since the fire was discovered.

\newline

(C) The area damaged by the fire is multiplied by

5

each minute.

Expression Structure: The expression given is $5 \times 1.15^{t}$ . To understand what the number $5$ represents, we need to consider the structure of the expression. The expression is in the form of $a \times 1.15^{t}$ , where ' $a$ ' is a constant multiplier and $1.15^{t}$ represents exponential growth over time ' $t$ '. The constant ' $a$ ' is the initial value before any growth has occurred.
Interpreting the Number $5$ : Since the expression represents the area damaged by a fire and the growth factor is $1.15^{(t)}$ , the number $5$ must represent the initial area that was damaged by the fire at the time it was discovered, before any additional damage occurred over time. This means that when $t=0$ , the area damaged is $5$ square meters.
Matching the Number $5$ to Answer Choices: Now, we can match our understanding of the number $5$ in the expression to the given answer choices. The correct choice is (A) An area of $5$ square meters had been damaged by the fire by the time it was discovered. This is because the number $5$ is the coefficient that represents the initial condition of the expression, which in this context is the initial area damaged by the fire.

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