Question

Suppose you are determining the growth rate of two species of plants. Species A is 12 cm tall and grows 2 cm per month. Species B is 10 cm tall and grows 3 cm per month. Which system of equations models the height of each species A(m) and B(m) as a function of months m.

A(m) = 12 + 2m
B(m) = 10 + 3m


A(m) = 2 + 12m
B(m) = 10 + 3m


A(m) = 12 + 2m
B(m) = 3 + 10m


A(m) = 2 + 12m
B(m) = 3 + 10m

Answer 1

Answer: First option:

A(m) = 12 + 2m

B(m) = 10 + 3m

Solution:

When you model a function y that depends on a veriable x, and you know the inicial value b, and the growth rate r, you can use this formula:

y=b+r x

We have two functions to model:

1) Species A is 12 cm tall and grows 2 cm per month:

y=A(m); b=12 cm; r=2 cm/month; x=m. Then:

Replacing in the equation:

y=b+r x

A(m)=12+2 m

2) Species B is 10 cm tall and grows 3 cm per month:

y=B(m); b=10 cm; r=3 cm/month; x=m. Then:

Replacing in the equation:

y=b+r x

B(m)=10+3 m