Question

1. a botanist compares the height of a type of plant in two different growing areas.

which statement best describes the results?
a. the height for both areas changes by a constant percent.
b. the height for both areas changes by a constant rate.
c. the height for area 1 changes by a constant percent while the height for area 2 changes at a constant rate.
d. the height for area 1 changes at a constant rate, while the height for area 2 changes by a constant percent.

Explanation:

Step1: Calculate growth - rate for Area 1

For Area 1, initial height $h_0 = 2$ cm at time $t = 0$. At $t = 1$, $h_1=3$ cm. The growth - factor from $t = 0$ to $t = 1$ is $\frac{3}{2}=1.5$. At $t = 2$, $h_2 = 4.5$ cm, and $\frac{4.5}{3}=1.5$. At $t = 3$, $h_3=6.75$ cm, and $\frac{6.75}{4.5}=1.5$. At $t = 4$, $h_4 = 10.125$ cm, and $\frac{10.125}{6.75}=1.5$. The height in Area 1 changes by a constant percent (50% growth each week since the growth - factor is 1.5).

Step2: Calculate growth - rate for Area 2

For Area 2, initial height $h_0 = 0$ cm at time $t = 0$. At $t = 1$, $h_1 = 6$ cm. At $t = 2$, $h_2=12$ cm, at $t = 3$, $h_3 = 18$ cm, at $t = 4$, $h_4=24$ cm. The change in height each week is $6$ cm. So the height in Area 2 changes at a constant rate of 6 cm per week.

Answer:

C. The height for Area 1 changes by a constant percent while the height for Area 2 changes at a constant rate.