Question

question 1-21
austin bought a tomato plant that was 16 centimeters (cm) tall. the plant is growing 1.5 centimeters per day. the height, h, of the plant can be modeled by ( h(d) = 16 + 1.5d ), where ( d ) represents the number of days since he bought the plant.
select all the true statements.
( h(2) = 4 )
( h(20) = 46 )
the tomato plant is 20 cm tall 20 days after austin bought it.
the tomato plant is 46 cm tall 20 days after austin bought it.
the tomato plant is 46 cm tall 30 days after austin bought it.
the tomato plant grows an additional 4 cm 32 days after austin bought it.

Explanation:

Step1: Analyze \( H(2) \)

Substitute \( d = 2 \) into \( H(d)=16 + 1.5d \).
\( H(2)=16+1.5\times2 = 16 + 3=19 \). So \( H(2)
eq4 \), first statement is false.

Step2: Analyze \( H(20) \)

Substitute \( d = 20 \) into \( H(d) \).
\( H(20)=16+1.5\times20 = 16 + 30 = 46 \). So \( H(20)=46 \), second statement is true.

Step3: Height at \( d = 20 \)

From Step2, \( H(20)=46 \) cm. So "the tomato plant is 46 cm tall 20 days after Austin bought it" is true.

Step4: Height at \( d = 32 \)

Substitute \( d = 32 \) into \( H(d) \).
\( H(32)=16+1.5\times32 = 16 + 48 = 64 \) cm. So "the tomato plant is 64 cm tall 32 days after Austin bought it" is true.

Step5: Check 49 cm at \( d = 22 \)

Substitute \( d = 22 \): \( H(22)=16+1.5\times22 = 16 + 33 = 49 \) cm. So "the tomato plant is 49 cm tall 22 days after Austin bought it" is true.

Step6: Additional growth by \( d = 32 \)

Initial height (\( d = 0 \)) is \( H(0)=16 \) cm. At \( d = 32 \), \( H(32)=64 \) cm. Additional growth: \( 64 - 16 = 48
eq4 \). So last statement is false.

Answer:

• \( H(20)=46 \) (true)
• The tomato plant is 46 cm tall 20 days after Austin bought it (true)
• The tomato plant is 64 cm tall 32 days after Austin bought it (true)
• The tomato plant is 49 cm tall 22 days after Austin bought it (true)