Question

Suppose you are determining the growth rate of two species of plants. Species A is 25 cm tall and grows 3 cm per month. Species B is 10 cm tall and grows 8 cm per month. Which system of equations models the height of each species H(m) as a function of months m.
H(m ) = 25 + 3m
H(m ) = 8 + 10m

H(m ) = 2 + 8m
H(m ) = 25 + 10m

H(m ) = 3 + 25m
H(m ) = 8 + 10m

H(m ) = 25 + 3m
H(m ) = 10 + 8m

Answer 1

If the growth rate is a constant, we can model it using a linear equation:

y = b + ax

where b = initial value, a = growth rate.
In this case, x = m = number of months.

Let's find the equation for the growth of each species.

Species A:
Initial height = b = 25 cm
Growth rate = a = 3 cm per month
So its height can be modeled by H(m) = 25 + 3m

Species B:
Initial height = b = 10 cm
Growth rate = a = 8 cm per month
So its height can be modeled by H(m) = 10 + 8m

Thus the answer is A: H(m) = 25 + 3m and B: H(m) = 10 + 8m.

Answer 2

Answer: Here we are assuming a constant growth of the plant, so we can think it as an linear relationship of the form H = a*m + b

where a is the amount of cm that the plant grows every month, m is the number of months, and b is the initial height of the plant.

then for the first plant we got: the initial height is 25 cm, and it grows 3 cm per month, then Ha(m) = 3cm*m + 25cm

For the second plant, the initial height is 10 cm, and grows 8 cm per month, then his equation is Hb(m) = 8cm*m + 10cm

Then the correct answer is the fourth option.