Maria and Jose have a large tomato garden. On day 1 when the tomatoes first ripened, they picked 3 tomatoes. Each day thereafter, as more tomatoes ripened, they doubled the number of tomatoes they picked. Let T be the number of tomatoes picked on day d. Which of the following best explains the relationship between d and T ? Choose 1 answer: (A) The relationship is exponential because T increases by 6 as d changes from d=1 to d=2. (B) The relationship is linear because T increases by a factor of 2 each time d increases by 1 . (C) The relationship is linear because T increases by 3 as d changes from d=0 to d=1. D The relationship is exponential because T increases by a factor of 2 each time d increases by 1 .

Day 1 Tomato Picking: On day 1, they picked 3 tomatoes. If they double the number of tomatoes they pick each day, then on day 2, they would pick 3 * 2 = 6 tomatoes.Day 2 Tomato Picking: On day 3, they would pick 6 * 2 = 12 tomatoes, which is doubling the amount from the previous day, not adding a fixed number.Day 3 Tomato Picking: This pattern shows that the number of tomatoes picked each day is not increasing by a fixed amount, but rather by a fixed ratio (doubling each day). This is a characteristic of an exponential relationship, not a linear one.Exponential Relationship Explanation: Therefore, the correct answer is that the relationship between d and T is exponential because T increases by a factor of 2 each time d increases by 1.

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Maria and Jose have a large tomato garden. On day $1$ when the tomatoes first ripened, they picked $3$ tomatoes. Each day thereafter, as more tomatoes ripened, they doubled the number of tomatoes they picked. Let $T$ be the number of tomatoes picked on day $d$ . Which of the following best explains the relationship between $d$ and $T$ ? $\newline$ Choose $1$ answer: $\newline$ (A) The relationship is exponential because $T$ increases by $6$ as $d$ changes from $d=1$ to $d=2$ . $\newline$ (B) The relationship is linear because $T$ increases by a factor of $2$ each time $d$ increases by $1$ . $\newline$ (C) The relationship is linear because $T$ increases by $3$ as $d$ changes from $d=0$ to $d=1$ . $\newline$ (D) The relationship is exponential because $T$ increases by a factor of $2$ each time $d$ increases by $1$ .

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Grade 7

Evaluate two-variable equations: word problems

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Q. Maria and Jose have a large tomato garden. On day

1

when the tomatoes first ripened, they picked

3

tomatoes. Each day thereafter, as more tomatoes ripened, they doubled the number of tomatoes they picked. Let

T

be the number of tomatoes picked on day

d

. Which of the following best explains the relationship between

d

and

T

\newline

Choose

1

answer:

\newline

(A) The relationship is exponential because

T

increases by

6

d

changes from

d=1

d=2

\newline

(B) The relationship is linear because

T

increases by a factor of

2

each time

d

increases by

1

\newline

T

increases by

3

d

changes from

d=0

d=1

\newline

(D) The relationship is exponential because

T

increases by a factor of

2

each time

d

increases by

1

Day $1$ Tomato Picking: On day $1$ , they picked $3$ tomatoes. If they double the number of tomatoes they pick each day, then on day $2$ , they would pick $3 \times 2 = 6$ tomatoes.
Day $2$ Tomato Picking: On day $3$ , they would pick $6 \times 2 = 12$ tomatoes, which is doubling the amount from the previous day, not adding a fixed number.
Day $3$ Tomato Picking: This pattern shows that the number of tomatoes picked each day is not increasing by a fixed amount, but rather by a fixed ratio (doubling each day). This is a characteristic of an exponential relationship, not a linear one.
Exponential Relationship Explanation: Therefore, the correct answer is that the relationship between $d$ and $T$ is exponential because $T$ increases by a factor of $2$ each time $d$ increases by $1$ .