Which of the following graphs could be a representation of a geometric sequence? Check all that apply
2 answers:
Answer:
Detailed explanation:
The formula that defines a geometric series is aₙ = a₁rⁿ⁻¹.
This parallels the exponential series y = a₀rⁿ.
A key distinction is that for geometric series, n must be a positive integer.
Consequently, the graph of a geometric series originates at some point on the y-axis and either escalates quickly or declines steadily toward the x-axis.
In Graph A, the resulting y values are 5/2⁰, 5/2¹, 5/2², and 5/2³, illustrating exponential decay.
In Graph B, the y values progress as 3¹, 3², and 3³, indicating exponential growth.
In Graph C, the y values are 2¹, 2², 2³, and 2⁴, which is also an example of exponential growth.
However, in Graph D, the y values show a steady increase of 1.5, making it an arithmetic series.
might represent a geometric series.
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Answer:
The hawk releases the prey from a height of 4 meters.
It takes the prey 4 seconds to reach the ground.
Step-by-step explanation:
The equation gives insights about the height of the prey at any time starting from the moment it is dropped. Thus, to determine the drop height, we evaluate the expression at time equals zero (the drop moment). This answers the first question:
To ascertain when the prey touches the ground, we set "h" to zero (height of zero) and solve for "t".
This results in a quadratic equation that can be solved via the quadratic formula:
Since negative time values are impractical, we select the positive 4 (4 seconds)