Question

A certain species of tree grows an average of 4.2 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 300 centimeters tall.

Answer 1

We know that the tree measures 300 cm at the start. We know that the tree is growing 4.2 cm each week.

So week one tree is this tall.

300cm + 4.2cm = 304.2 cm

Week two the tree is this tall.

300cm + 4.2cm + 4.2cm = 308.4 cm

Week three the tree is this tall.

300cm + 4.2cm + 4.2cm + 4.2cm = 312.6cm

So we start to see a pattern here. We should also note, that when we add the same number over and over again, that's multiplication.

So 4.2cm + 4.2cm is the same as 2 times 4.2cm. For two weeks of growth.

And 4.2cm + 4.2cm + 4.2cm is the same as 3 times 4.2cm. For three weeks of growth.

Answer 2

So it looks like we just multiply the number of weeks times 4.2cm and add in the 300cm tree started at, we would get the tree's height for that number of weeks.

So if we let w= the number weeks, our equation would look like this:

300cm + w(4.2cm)= height of the tree

or if we let h=height of the tree we have this:

300cm + w(4.2.cm)=h