Question

When it hatches from its egg, the shell of a 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 shells does a fully grown crab have during its life

Answer 1

The size of the n'th shell is (4/3)^(n-1) cm. We want to find the value of n that makes (4/3)^(n-1) = 10. If you've done logarithms, that's pretty easy: n-1 = log 10 / log (4/3) = 8.003, i.e. n = 9 (to nearest integer). So a fully grown crab has 9 shells.
If you haven't done logarithms, the easiest thing is to make a table :
Shells Size (cm)
1) 1
2) 4/3 ≈ 1.33
3) 16/9 ≈ 1.78
4 ) 64/27 ≈ 2.37
5) 256/81 ≈ 3.16
... .........
9 ) 65536/6561 ≈ 9.99

Answer 2

Answer : 9 Shells

Step-by-step explanation: it starts at 1cm

growth rate = 1/3

fully grown size or final outcome = 10cm

10-1^1/3

=9 shells

the shell grows one-third, and the final size is 10, so if we subtract 1 (starting size) to the power one-third(the size it grows each time) and then subtract it by 10 (the final size) we get the amount of times it it grows, which is 9.