# Algebra

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This question deals with Exponential Growth and Decay Test. Question:Consider the following:Start by tossing 30 dice. Then remove the dice that show 5s and 6s and toss the remaining dice. Repeat this process until you only have 2 dice remaining. The data in the table were collected by running the above experiment.

Toss Number = 0,# of dice remaining=30
Toss Number = 1,# of dice remaining=20
Toss Number = 2,# of dice remaining=15
Toss Number = 3,# of dice remaining=11
Toss Number = 4,# of dice remaining=8
Toss Number = 5,# of dice remaining=6
Toss Number = 6,# of dice remaining=4
Toss Number = 7,# of dice remaining=3
Toss Number = 8,# of dice remaining=2

Estimate the best function rule to model this data. Give your answer in the form of y=a(b^x)

(^x meaning exponent)

• Algebra -

each toss on the average you eliminate 2 of the 6 sides
so
N(t+1) = n(t) * 4/6

in continuous form
dN/dt = -(2/6) N
of course 2/6 is 1/3

solution of form N = No e^kt
where No = 30
dN/dt = kNo e^kt
so k=-1/3
try
N = 30 e^-(t/3)

for example if t = 6
N = 30 e^-2
N = 4.06

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