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Questions and Answers
What is the formula for exponential growth?
What is the formula for exponential growth?
- y=a(1+r)^t (correct)
- y=a(1-r)^t
- x = -b ± √(b² - 4ac)/2a
- b^2-4ac
What is the formula for exponential decay?
What is the formula for exponential decay?
- x = -b ± √(b² - 4ac)/2a
- b^2-4ac
- y=a(1-r)^t (correct)
- y=a(1+r)^t
What does the Quadratic Formula calculate?
What does the Quadratic Formula calculate?
x = -b ± √(b² - 4ac)/2a
Match the discriminant rules with their outcomes:
Match the discriminant rules with their outcomes:
What is the discriminant formula?
What is the discriminant formula?
What does 'b' represent in the context of a function?
What does 'b' represent in the context of a function?
Complete the sentence: For m: as x ___ 1, y ___ m.
Complete the sentence: For m: as x ___ 1, y ___ m.
What is the term for the x-intercept?
What is the term for the x-intercept?
What does 'Minimum' refer to in a function?
What does 'Minimum' refer to in a function?
What does 'Maximum' refer to in a function?
What does 'Maximum' refer to in a function?
What is the characteristic of Linear Growth?
What is the characteristic of Linear Growth?
What characterizes exponential growth?
What characterizes exponential growth?
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Study Notes
Exponential Growth and Decay
- Exponential Growth Formula: y = a(1 + r)^t, where 'a' is the starting value, 'r' is the growth rate, and 't' is time.
- Exponential Decay Formula: y = a(1 - r)^t, affecting the same variables as growth but indicating a decrease.
Quadratic Functions
- Quadratic Formula: x = -b ± √(b² - 4ac)/2a, used to find the roots of quadratic equations.
- Discriminant Formula: d = b² - 4ac, determines the nature of the roots based on its value.
Discriminant Rules
- Two Solutions: Occurs when d > 0, meaning there are two distinct real solutions.
- No Solutions: When d < 0, indicating that there are no real solutions.
- One Solution: Happens when d = 0, resulting in exactly one real solution.
Characteristics of Functions
- 'b' as Starting Value: In the context of exponential functions, 'b' indicates the initial value of 'y'.
- Rate of Change: For a constant m, as 'x' increases by 1, 'y' increases by m, representing a linear growth scenario.
Features of Graphs
- Zero (x-intercept): The point where the graph intersects the x-axis, indicating where y equals zero.
- Minimum Value: Refers to the lowest y-value achieved on the graph, indicating the lowest point of the function.
- Maximum Value: Denotes the highest y-value on the graph, representing the peak of the function.
Growth Models
- Linear Growth: Characterized by a consistent increase of the same amount over intervals.
- Exponential Growth: Features a changing increase, where the addition grows disproportionately over time, highlighted by the growth formula.
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