When it hatches from its egg, the shell of certain crab is 1cm across. When fully grown the shell is approximately 10cm across. Each new shell is one-third bigger than the previous one. How many shell does a fully grown carb have during its life?

Well every time it gets rid of a shell it grows 1 1/3 times larger. So so to see how much it grows after the first time you say

1 cm * 1 1/3 = 1 1/3 cm

to get the next one you do the same

1 1/3 cm * 1 1/3 cm = 16/9

It will keep going multiplying by 1 1/3. So so we can say in an equation that the

(initial size) * 1 1/3 * (number of shells) = length

Or 1cm * 1 1/3 * n = L

We we know the final length is 10cm

So 1 1/3 * n = 10cm

n = 7.5shells

so approximately 7 or 8 shells