Consider the following experiment. Start by tossing 30 dice.Then remove the dice that show 5s and 6s and toss the remaining dice.Repeat until you have 2 dice remaining.
toss # 0 1 2 3 4 5 6 7 8
# of dice 30 20 15 11 8 6 4 3 2
Estimate the best function rule to model this data. Answer should be in the form of y=a(bx)
http://www.jiskha.com/display.cgi?id=1263789491
To estimate the best function rule to model the given data, we can first observe the pattern in the data and then use a process of elimination to determine the possible function rule.
From the given data, we see that after each toss, the number of dice decreases. Specifically, the number of dice in each toss can be approximated as y = a(b^x), where x represents the toss number and y represents the number of dice remaining.
Let's analyze the data:
toss # 0 1 2 3 4 5 6 7 8
# of dice 30 20 15 11 8 6 4 3 2
From the data, we can notice that the number of dice decreases by a factor of 2 after each toss. This suggests that b = 2. Now, we need to find the value of a.
To find the value of a, we can choose any toss and substitute the values of x, y, and b into the function y = a(b^x) and solve for a. Let's choose the first toss (x = 0, y = 30) and substitute the values:
30 = a(2^0)
30 = a(1)
30 = a
So, a = 30.
Therefore, the best function rule to model this data is:
y = 30(2^x)
In the form y = a(b^x), the function rule is:
y = 30(2^x)