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Fang and Meng have a large rose garden. When the roses first bloomed, they initially picked 4 fresh roses. Each day thereafter, as more roses bloomed, they quadrupled the number of roses they picked. Let
R be the number of roses picked on day
t. Which of the following best explains the relationship between
t and
R ?
Choose 1 answer:
(A) The relationship is exponential because the values of
R always increase as the values of
t increase.
(B) The relationship is linear because the values of
R always increase as the values of
t increase.
(C) The relationship is linear because the values of
R are always even integers.
(D) The relationship is exponential because
R increases by a factor of 4 each time
t increases by 1 .

Fang and Meng have a large rose garden. When the roses first bloomed, they initially picked $4$ fresh roses. Each day thereafter, as more roses bloomed, they quadrupled the number of roses they picked. Let $R$ be the number of roses picked on day $t$ . Which of the following best explains the relationship between $t$ and $R$ ? $\newline$ Choose $1$ answer: $\newline$ (A) The relationship is exponential because the values of $R$ always increase as the values of $t$ increase. $\newline$ (B) The relationship is linear because the values of $R$ always increase as the values of $t$ increase. $\newline$ (C) The relationship is linear because the values of $R$ are always even integers. $\newline$ (D) The relationship is exponential because $R$ increases by a factor of $4$ each time $t$ increases by $1$ .

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Find a value using two-variable equations: word problems

Full solution

Q. Fang and Meng have a large rose garden. When the roses first bloomed, they initially picked

4

fresh roses. Each day thereafter, as more roses bloomed, they quadrupled the number of roses they picked. Let

R

be the number of roses picked on day

t

. Which of the following best explains the relationship between

t

and

R

?

\newline

Choose

1

answer:

\newline

(A) The relationship is exponential because the values of

R

always increase as the values of

t

increase.

\newline

(B) The relationship is linear because the values of

R

always increase as the values of

t

increase.

\newline

(C) The relationship is linear because the values of

R

are always even integers.

\newline

(D) The relationship is exponential because

R

increases by a factor of

4

each time

t

increases by

1

.

Day $1$ : Picking $4$ Roses: On day $1$ , they picked $4$ roses. If they quadruple the number of roses they pick each day, then on day $2$ , they would pick $4 \times 4 = 16$ roses.
Day $2$ : Quadrupling Roses: On day $3$ , they would pick $16 \times 4 = 64$ roses. This pattern shows that the number of roses picked each day is multiplied by $4$ from the previous day.
Day $3$ : Multiplying by $4$ : This means that the number of roses picked is not increasing by a constant amount each day, but rather by a constant factor. This is a characteristic of an exponential function, not a linear one.
Exponential Relationship Explanation: Therefore, the correct answer is (D) The relationship is exponential because $R$ increases by a factor of $4$ each time $t$ increases by $1$ .

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\newline

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