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(22) = 4
☐ h(22) = 49
☐ the tomato plant is 20 cm tall 22 days after austin bought it.
☐ the tomato plant is 65 cm tall 22 days after austin bought it.
☐ the tomato plant is 49 cm tall 22 days after austin bought it.
☑ the tomato plant grows an additional 4 cm, 22 days after austin bought it.

Explanation:

Step1: Analyze \( H(22) \)

Given \( H(d) = 16 + 1.5d \), substitute \( d = 22 \):
\( H(22)=16 + 1.5\times22 \)
\( =16 + 33 \)
\( = 49 \). So \( H(22)=49 \) is correct.

Step2: Check height at 22 days

From Step1, \( H(22)=49 \) cm. So "The tomato plant is 49 cm tall 22 days after..." is correct.

Step3: Check growth in 22 days

Growth per day is 1.5 cm, so in 22 days: \( 1.5\times22 = 33 \) cm. Wait, wait—wait, original height is 16 cm. Wait, no: the growth from day 0 to day 22 is \( H(22)-16 = 49 - 16 = 33 \)? Wait, no, the option says "grows an additional 4 cm"—wait, no, maybe miscalculation? Wait, no, let's recheck:

Wait, the option "The tomato plant grows an additional 4 cm, 22 days after..."—no, 1.5×22=33. Wait, maybe the option was misread. Wait, the correct ones:

• \( H(22)=49 \) (so "H(22)=49" is correct).
• "The tomato plant is 49 cm tall 22 days after..." is correct.

Wait, let's re-express:

1. \( H(22)=16 + 1.5(22)=16 + 33 = 49 \). So:

• \( H(22)=4 \): Wrong (4≠49).
• \( H(22)=43 \): Wrong (43≠49).
• "20 cm tall": Wrong (20≠49).
• "65 cm tall": Wrong (65≠49).
• "49 cm tall": Correct.
• "grows an additional 4 cm": Wait, 1.5×22=33, so growth is 33 cm. But maybe the option was a typo? Wait, no—wait, the last option (partially visible) might have a typo, but from the calculations:

Correct statements:

• \( H(22)=49 \) (the checkbox for \( H(22)=49 \) is correct).
• "The tomato plant is 49 cm tall 22 days after Austin bought it." (correct).

Answer:

• \( \boldsymbol{H(22) = 49} \) (the checkbox for this is correct).
• "The tomato plant is 49 cm tall 22 days after Austin bought it." (this statement is correct).