According to an article published by J.M.J. Van leenween (a physicist at leiden

Question

According to an article published by J.M.J. Van leenween (a physicist at leiden unvirsity in the neatherlands),a standard domino is able to knock over a domino which is 1.5 times the height of the original domino.

This means that a domino which is 10 centimeters tall can knock over a donimo that is that is 15 centimeters tall,and a 15 centemeter tall domino can knock down a 22.5 centemer tall domino.

A) Suppose our intial domino is 3 centimeters and each donimo after that is 1.5 times as large.Create a funtion F(x) which will tell the hieght (in cm)is of the Xth donimo.

B) How tall will the 20th donimo be?

C)Find the inverse F-1(x) for the funtion created in part a.

D)What does the domain Of F-1(X) represent?what does the range represent of F-1(X) represnt?

E) According to the guiness world record the worlds longest measured sausage 62.6 kilometers .Which donimo from part A will be as tall as the worlds longest sausage?

Explanation / Answer

initial domino is 3 cm

and each domino after that is 1.5 times as large

f(x) = 1.5x + 3

where x is the number of domino

b) 20 th domino would be

f(x) = 1.5(20) + 3

= 33 cm

c) f^-1 (x) = ( x- 3 ) / 1.5

d) domain of f^-1 (x) represents that minimum height of domino is 3cm

range of f^-1 (x) represents minimum number of dominos is 0

e) 62600 = 1.5x + 3

x = 41731

so, domino 41731 represents worlds longest sausage

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