i'm supposed to make an equation going off of this problem.. it is supposed to be an exponential equation, but i don't exactly know how i am supposed to do this.. please help:(..
You roll 36 dice and remove the dice with one dot showing. You roll the remaining dice and remove the dice with one dot showing. You roll the remaining dice and remove the dice with one dot showing. Repeat this process until you have no dice left. (x=roll number, y=number of dice remaining).
Exponential equation? Hardly.
See question 8 here.
http://www.madandmoonly.com/doctormatt/mathematics/dice1.pdf
well i'm supposed to come to an equation of y=(5/6)^x (36) but i don't even understand how u end up with that
To create an exponential equation for this problem, we need to understand the relationship between the roll number (x) and the number of dice remaining (y).
Let's break down the problem step by step:
Step 1: You start with 36 dice.
Step 2: After the first roll, you remove the dice with one dot showing.
Step 3: You roll the remaining dice and remove the dice with one dot showing again.
Step 4: Repeat step 3 until there are no dice left.
Based on this process, we can see that the number of dice remaining decreases by a certain factor with each roll. In this case, the factor is the probability of rolling a dice with one dot.
To create an exponential equation, we can use the general form: y = a * b^x, where a is the initial value, b is the common ratio, and x is the variable representing the roll number.
In this problem, the initial value is 36 (the number of dice we start with), and the common ratio (b) is the probability of rolling a dice with one dot. To find this probability, we need to know the total number of dots on all six sides of a dice, which is 21 (1 + 2 + 3 + 4 + 5 + 6).
The probability of rolling a dice with one dot showing is 1/21. Therefore, we can replace b with 1/21 in our equation.
The equation becomes: y = 36 * (1/21)^x
This exponential equation will give you the number of dice remaining (y) after each roll (x).