33 inches per year
in half a year, the sunflower grew 37 -20 1/2 = 16 1/2 inches. your proportion is
(16 1/2 inches)/(1/2 year) = g/(1 year) . . . . where g is the yearly growth
multiplying by 1 year and simplifying, you can find g to be
g = (33/2 inches)/(1/2) = 33 inches
that is, the growth rate is 33 inches per year.
comment on the solution technique
i personally find a proportion to be unnecessary. when you want to find the rate of x per y, divide the amount of x you are given by the amount of y you are given.
here, you are given a growth of 16 1/2 inches in 1/2 year, so you simply perform the division (16 1/2 inches)/(1/2 year) = 33 inches/year.
hello from mrbilldoesmath!
first glance at the numbers shows each term is 1 larger than the preceding terms. so we are adding the constant 1 to each term to get the next term. this is an arithmetic progression.