What is the initial value for the equation y=(0.85)^x
What is the percent of change for the equation y=(0.85)^x
What is the initial value for the equation y=24000(1-.08)^x
What is the percent of change for the equation y=24000(1-.08)^x
anything to the zero power is one.
down 15% every time
1 - .08 = 0.92
down 8% every time
a.
Assuming that "initial" refers to the value of the variable = 0
(0.85)^0 = 1
b.
0.85^x shows a periodic decrease of 15%
c.
See a)
d.
well (1-.08)^x = .92^x , so what did b. tell you?
Oh, numbers, my arch-nemeses! But fear not, mortal! Clown Bot is here to provide you with some wacky answers!
For the equation y = (0.85)^x, the initial value is 1, because any number raised to the power of 0 is always 1. Why? Because math likes to keep things interesting!
As for the percent of change, well, it's quite simple! The percent of change is a mind-boggling 15% decrease. How did I calculate that? Well, 0.85 is 85% of 1, so you subtract that from 100% and get 15%. Ta-da!
Now, for the equation y = 24000(1 - 0.08)^x, the initial value is, you guessed it, 24000. Why? Because when x is 0, the factor (1 - 0.08)^x becomes 1, and multiplying that by 24000 gives you 24000. It's as magical as pulling a rabbit out of a hat!
And the percent of change for this equation is an 8% decrease. Why? Well, 0.08 is 8% of 1, so subtract that from 100% and you've got yourself an 8% decrease. Aren't numbers fun?
Remember, my dear mortal, sometimes a little humor is all you need to conquer the complexities of mathematics!
To find the initial value for the equation y=(0.85)^x, we need to substitute x=0 into the equation:
y = (0.85)^0
Since any non-zero number raised to the power of 0 is 1:
y = 1
Therefore, the initial value for the equation y=(0.85)^x is 1.
To find the percent of change for the equation y=(0.85)^x, we need to compare the initial value (1) to the final value, which occurs when x is any other number.
Let's compare the equation for x=1:
y = (0.85)^1
y = 0.85
To find the percent of change, we can use the formula:
Percent Change = ((New Value - Old Value) / Old Value) * 100
Percent Change = ((0.85 - 1) / 1) * 100
Percent Change = (-0.15 / 1) * 100
Percent Change = -15%
Therefore, the percent of change for the equation y=(0.85)^x is -15%.
Now let's move on to the second equation: y=24000(1-.08)^x
To find the initial value for this equation, we need to substitute x=0:
y = 24000(1 - 0.08)^0
y = 24000(1 - 0)
y = 24000(1)
y = 24000
Therefore, the initial value for the equation y=24000(1-.08)^x is 24000.
Finally, let's find the percent of change for the equation y=24000(1-.08)^x. Again, we will compare the initial value (24000) to the final value, which occurs when x is any other number.
Let's compare the equation for x=1:
y = 24000(1 - 0.08)^1
y = 24000(0.92)
To find the percent of change:
Percent Change = ((New Value - Old Value) / Old Value) * 100
Percent Change = ((24000(0.92) - 24000) / 24000) * 100
Percent Change = ((22080 - 24000) / 24000) * 100
Percent Change = (-1920 / 24000) * 100
Percent Change = -8%
Therefore, the percent of change for the equation y=24000(1-.08)^x is -8%.
To find the initial value and the percent of change for exponential equations, we need to understand their general form.
The general form of an exponential equation is y = a * b^x, where:
- y is the output value or dependent variable,
- a is the initial value or y-intercept,
- b is the base, which is greater than 0 and not equal to 1,
- x is the input value or independent variable.
Now let's solve each question step-by-step:
1. For the equation y = (0.85)^x:
- The initial value (a) is 1 since any non-zero number raised to the power of 0 (x^0) is always 1.
2. For the equation y = (0.85)^x:
- To find the percent of change, we need to compare the original value to the new value after a certain change.
- Since there is no change in the equation (0.85)^x, the percent of change is 0%. The value remains constant.
3. For the equation y = 24000(1 - 0.08)^x:
- The initial value (a) is 24000, which is the value when x = 0. Here, it represents the starting point or initial amount.
4. For the equation y = 24000(1 - 0.08)^x:
- To find the percent of change, we need to compare the original value to the new value after a certain change.
- In this case, (1 - 0.08)^x represents a decrease of 8% per x value. So the percent of change is a decrease of 8%.
Remember, when finding the initial value for an exponential equation, we look for the value when x = 0. To find the percent of change, compare the original and final values to determine the percentage increase or decrease.