Mathematics

Problem

A machine part wears down in such a way that its thickness each day forms a geometric progression. On the first day its thickness is 800 micrometres and each subsequent day it retains only

\dfrac{3}{4}

of the previous day’s thickness. (i) Obtain an expression for the thickness on the

n^{\text{th}}

day. (ii) Calculate the smallest integer

n

for which the thickness will become less than 5 micrometres. a. Obtain an expression for the thickness on the

n^{\text{th}}

day. b. Calculate the smallest integer

n

for which the thickness is less than 5 micrometres.

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