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
It looks to me that the denominator is 2^(n-1)/100 for n=1, 2, 3, 4, 5, ,,,,
idk ask someone else
To figure out the pattern, let's analyze the relationship between the given numbers.
Notice that as the input value increases by 1, the output value doubles. We can represent this relationship using an algebraic expression.
Let's call the input value "x" and the output value "y".
The pattern can be expressed using the equation:
y = 0.01 * 2^(x-1)
In this equation, 0.01 represents the starting value and 2 represents the factor by which the output doubles. (x-1) accounts for the fact that the first term is 1, not 0.
Let's test this equation:
For x = 1, the equation gives: y = 0.01 * 2^(1-1) = 0.01 * 2^0 = 0.01 * 1 = 0.01
For x = 2, the equation gives: y = 0.01 * 2^(2-1) = 0.01 * 2^1 = 0.01 * 2 = 0.02
For x = 3, the equation gives: y = 0.01 * 2^(3-1) = 0.01 * 2^2 = 0.01 * 4 = 0.04
Continuing this pattern, you can plug in any value for x to find the corresponding output value, y.
For example, for x = 25, the equation gives: y = 0.01 * 2^(25-1) = 0.01 * 2^24 = 0.01 * 16,777,216 = 153,948.16
So the algebraic expression for the given pattern is: y = 0.01 * 2^(x-1)