Question

Nara got two new plants for her apartment. Each plant grew at a constant rate.

The height (in centimeters) of the first plant as a function of time (in days since Nara got it) is given by the following table of values:

Time\text{Time}Timestart text, T, i, m, e, end text (days) Height\text{Height}Heightstart text, H, e, i, g, h, t, end text (centimeters)

10 34

15 36

20 38

The graph of the height (in centimeters) of the second plant as a function of time (in days since Nara got it) is shown below.

Which plant was taller when Nara got the plants?

Choose 1 answer:

Choose 1 answer:


(Choice A)

A

The first plant

(Choice B)

B

The second plant

(Choice C)

C

They were equally tall


Which plant grew faster?

Choose 1 answer:

Choose 1 answer:


(Choice A)

A

The first plant

(Choice B)

B

The second plant

(Choice C, Checked)

C

They both grew at the same rate

Answer 1

The answer is C. They were equally tall and B. The second plant.

Explanation:

I got this answer from Khan Academy.

Hope this helps! :)

Answer 2

Which plant was taller when Nara got the plants? C. They were equally tall

Which plant grew faster? B. The second plant

Explanation:

Slope of the first plant :

m = (y2 - y1)/(x2- x1)

m = (36 - 34)/(15 - 10) = 0.4

y-intercept of the first plant :

y = m*x + b

b = y1 - m*x1

b = 34 - 0.4*10 = 30

From the picture we can see that the y-intercept of the second plant is 30 cm

Y-intercept represents plant heights when Nara got the plants; then they were equally tall

From the picture we can see that second plant grew 2 cm in 2 days; then its slope is 2/2 = 1

Slope measures how fast each plant grew; then the second plant grew faster