Which set of ordered pairs could be generated by an exponential function
Answers
The required set of ordered pairs are (0, 1), (1, 3), (2, 9), (3, 27). The correct option is (D).
What is an exponential function?
An exponential function can be represented as y = aˣ. When x = 0, y = a⁰ = 1. The range of an exponential function is from zero to infinity for a > 0.
It is clear from the given options that, only options (B) and (D) satisfies the general expression y = aˣ at x = 0.
Now, both these options can be examined one by one as follows,
Option (B),
The ordered pairs are given as (0, 1), (1, 2), (2, 5), (3, 10).
Substitute the values in the general expression y = aˣ, first two pair are satisfied for a = 2 but the remaining two are not.
Option (D),
The ordered pairs are given as (0, 1), (1, 3), (2, 9), (3, 27).
Substitute the values in the general expression y = aˣ, all the pairs are satisfied for a = 3.
Thus, the correct option is found.
Hence, the set of ordered pairs which could be generated by an exponential function are (0, 1), (1, 3), (2, 9), (3, 27).
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Answer:
C is the answer
Step-by-step explanation:
If you graph them on a line the outcome will be a straight line making it functional and a proportion
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B. They scored 27 points.
C. Eighty miles per hour.
D. Half the speed of the car.
Answers
A. The number of different colors on the page.
D. Half the speed of the car.
These statements contain variables representing unknown quantities or values.
Variables in mathematics and science are symbols that represent unknown values or quantities. Let's analyze each statement to identify the ones containing variables:
A. "The number of different colors on the page."
This statement contains a variable because it represents an unknown quantity, the number of colors.
B. "They scored 27 points."
This statement does not contain a variable as it explicitly states a specific value (27 points).
C. "Eighty miles per hour."
This statement does not contain a variable as it provides a specific constant value (80 miles per hour).
D. "Half the speed of the car."
This statement contains a variable because it represents an unknown value, which would depend on the actual speed of the car.
In summary, the statements containing variables are:
A. The number of different colors on the page.
D. Half the speed of the car.
These statements represent quantities that can vary, making them suitable for mathematical or scientific analysis where variables are used to express relationships and solve equations.
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A) the number of different colors on the page; and
D) half the speed of the car.
Explanation:
A variable represents an unknown amount.
For A, we do not know how many colors are on the page; this means we would use a variable to represent it.
For D, while we know we want half of the speed of the car, we do not know what the speed of the car actually is; therefore we would use a variable to represent it.
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