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)

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

To model this data using an exponential function, we need to find the values of 'a' and 'b' in the equation y = a(b^x).

Looking at the provided data, we can observe that as the toss number increases, the number of dice remaining decreases. This suggests that the data exhibits exponential decay.

To find the values of 'a' and 'b', we can use the initial and final data points from the table.

From the table, we see that at toss number 0, there are 30 dice remaining. This gives us the point (0, 30).
At the final toss number 8, there are 2 dice remaining. This gives us the point (8, 2).

Now, let's plug these points into the equation y = a(b^x) and solve for 'a' and 'b'.

Using the point (0, 30):
30 = a(b^0)
30 = a(1)
a = 30

Using the point (8, 2):
2 = 30(b^8)
Solve for b using logarithms:
2/30 = (b^8)
log(2/30) = 8log(b)
log(b) = log(2/30)/8
log(b) ≈ -0.085

Now, solve for b:
b ≈ 10^(-0.085)
b ≈ 0.803

Therefore, the best function rule to model this data is y = 30(0.803^x).