A landscaping company sells bags that hold up to $2.3 \text{ cubic feet } (\text{ft}^{3})$ of mulch. The company guarantees that there is at least $2\text{ft}^{3}$ of mulch inside each bag. Which of the following functions gives the nonnegative difference between the maximum and minimum mulch volumes, in cubic feet, that could be contained in $b$ bags purchased from the landscaping company? $\newline$ Choose $1$ answer: $\newline$ (A) $f(b)=0.3b$ $\newline$ (B) $f(b)=2b$ $\newline$ (C) $f(b)=2.3b$ $\newline$ (D) $f(b)=4.3b$

View step-by-step help

Home

Math Problems

Grade 6

Powers with fractional bases

Full solution

Q. A landscaping company sells bags that hold up to

2.3 \text{ cubic feet } (\text{ft}^{3})

of mulch. The company guarantees that there is at least

2\text{ft}^{3}

of mulch inside each bag. Which of the following functions gives the nonnegative difference between the maximum and minimum mulch volumes, in cubic feet, that could be contained in

b

bags purchased from the landscaping company?

\newline

Choose

1

answer:

\newline

(A)

f(b)=0.3b

\newline

(B)

f(b)=2b

\newline

(C)

f(b)=2.3b

\newline

(D)

f(b)=4.3b

Identify volumes per bag: Identify the maximum and minimum volumes of mulch per bag. The maximum volume per bag is given as $2.3$ cubic feet. The minimum volume per bag is guaranteed to be at least $2$ cubic feet.
Calculate volume difference: Calculate the difference in volume for one bag. $\newline$ The difference between the maximum and minimum volume per bag is $2.3 \, \text{ft}^3 - 2 \, \text{ft}^3 = 0.3 \, \text{ft}^3$ .
Determine total difference function: Determine the function that represents the total difference for $b$ bags. $\newline$ Since the difference per bag is $0.3$ cubic feet, for $b$ bags, the total difference would be $0.3 \text{ ft}^3$ multiplied by the number of bags $b$ . $\newline$ Therefore, the function is $f(b) = 0.3 \times b$ .