Question

A tree is growing at a rate of 36 feet every 3

Answer 1

well, we know the tree is growing at a rate of 36 feet every 3 years, how many feet is that in 1 year alone?   well, simply 36/3 = 12.

so the tree is growing 12 feet per year.

when it was first planted, it was 5 feet tall, and then after every year, we have to add 12 feet subsequently, let's do that

year 1 .......... 5 + 12(1)

year 2 .......... 5 + 12(2)

year 3 .......... 5 + 12(3)

year 4 .......... 5 + 12(4)

year 5 .......... 5 + 12(5)

year 6 .......... 5 + 12(6)

year 7 .......... 5 + 12(7)

year y .......... 5 + 12(y)

$\bf \stackrel{\textit{height}}{h}~~=~~\stackrel{\textit{initial height}}{5}~~+~~\stackrel{\textit{yearly rate}}{12y} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{tree is now}}{77} = 5 + 12y\implies 72=12y\implies \cfrac{72}{12}=y\implies \boxed{6=y}$