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Dyami planted a palm tree in the back yard of his house several years ago. Initially it was 200 centimeters high and its height increased by 30 centimeters each year. Let
H be the height of the tree in centimeters
t years after it was planted. Which of the following best explains the relationship between
t and
H ?
Choose 1 answer:
(A) The relationship is exponential because
H increases by a factor of 30 each time
t increases by 1 .
(B) The relationship is linear because
H increases by 30 each time
t increases by 1 .
(C) The relationship is exponential because
H always increases as
t increases.
(D) The relationship is linear because
H increases by 200 each time
t increases by 1 .

Dyami planted a palm tree in the back yard of his house several years ago. Initially it was $200$ centimeters high and its height increased by $30$ centimeters each year. Let $H$ be the height of the tree in centimeters $t$ years after it was planted. Which of the following best explains the relationship between $t$ and $H$ ? $\newline$ Choose $1$ answer: $\newline$ (A) The relationship is exponential because $H$ increases by a factor of $30$ each time $t$ increases by $1$ . $\newline$ (B) The relationship is linear because $H$ increases by $30$ each time $t$ increases by $1$ . $\newline$ (C) The relationship is exponential because $H$ always increases as $t$ increases. $\newline$ (D) The relationship is linear because $H$ increases by $200$ each time $t$ increases by $1$ .

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Write and solve equations for proportional relationships

Full solution

Q. Dyami planted a palm tree in the back yard of his house several years ago. Initially it was

200

centimeters high and its height increased by

30

centimeters each year. Let

H

be the height of the tree in centimeters

t

years after it was planted. Which of the following best explains the relationship between

t

and

H

?

\newline

Choose

1

answer:

\newline

(A) The relationship is exponential because

H

increases by a factor of

30

each time

t

increases by

1

.

\newline

(B) The relationship is linear because

H

increases by

30

each time

t

increases by

1

.

\newline

(C) The relationship is exponential because

H

always increases as

t

increases.

\newline

(D) The relationship is linear because

H

increases by

200

each time

t

increases by

1

.

Initial Height: Initial height of the palm tree, $H_{\text{initial}} = 200\,\text{cm}.$
Height Increase: Height increase per year, $H_{\text{increase}} = 30\,\text{cm}$ .
Total Height Equation: Total height after $t$ years, $H = H_{\text{initial}} + (H_{\text{increase}} \times t)$ .
Substitution: Substitute the given values into the equation: $H = 200 + (30 \times t)$ .
Linear Relationship: The relationship between $H$ and $t$ is linear because the height increases by a constant amount each year.
Correct Answer: The correct answer is (B) The relationship is linear because $H$ increases by $30$ each time $t$ increases by $1$ .

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