I need to figure out a pattern (using an algebraic expression) that will get me from: 1 to .01, 2 to .02, 3 to .04, 4 to .08, etc. all the way to 25 to 153,948.16! HELP
To determine the pattern, let's analyze the given pairs of numbers. We can observe that the second number is obtained by multiplying the first number by some factor each time.
Let's call the first number in each pair "x" and the second number "y". We want to find an algebraic expression in terms of "x" to obtain "y".
From the given pairs, we can see that the factor increases each time. It starts with 0.01 (1/100), then doubles to 0.02 (1/50), then doubles again to 0.04 (1/25), and so on.
So, the general pattern is that the factor doubles with each successive pair. To represent this in an algebraic expression, we can use the formula:
y = (1/100) * (2^(x-1))
In this expression, (x-1) ensures that when x = 1, we get the first number in the sequence, 0.01. The factor 1/100 represents the initial value, and 2 is the base for the doubling.
Now, let's check if this pattern holds for all the given numbers:
For x = 1,
y = (1/100) * (2^(1-1))
y = (1/100) * (2^0) = 1 * 1 = 1
For x = 2,
y = (1/100) * (2^(2-1))
y = (1/100) * (2^1) = 1/100 * 2 = 0.02
For x = 3,
y = (1/100) * (2^(3-1))
y = (1/100) * (2^2) = 1/100 * 4 = 0.04
By repeating this process for the remaining values of x, you will see that the pattern continues to hold.
So, the algebraic expression that represents the given pattern is:
y = (1/100) * (2^(x-1))