Several ordered pairs from a continuous exponential function are shown in the table.
2 answers:
Answer:
The function's domain is all real numbers, represented as {x: x ∈ R}, while the range consists of positive y values, depicted as {y: y > 0}
Step-by-step explanation:
* Let's go through the problem-solving steps
- The standard equation for a continuous exponential function can be expressed as
where 'a' signifies the starting value and 'k' denotes the growth factor
- We have several ordered pairs derived from the continuous exponential
function
- The ordered pairs include:
(0, 4), (1, 5), (2, 6.25), (3, 7.8125)
- We will substitute the x and y values into the equation to determine 'a,'
∵
∵ For the first ordered pair where x = 0 and y = 4
- Insert x and y into the equation
∴
∴
- This results in = 1
∴ Hence, a = 4
- Next, we substitute this value of 'a' back into the equation
∴
∵ In the first ordered pair where x = 1 and y = 5
- Insert these x and y values into the equation
∴
∴
- Now, divide both sides by 4
∴ = 1.25
- Substitute the computed value into the equation
- The domain encompasses all x values that make the function valid
- The range includes y values that correspond to x
∵ The function does not become undefined for any x value
∴
Thus, the domain is all real numbers∵ y is never negative
∴
Consequently, the range is all positive real numbers
*
The function's domain consists of {x: x ∈ R}, while the range consists of {y: y > 0}
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Answer:
The appropriate answer is 72 + 4 × x 400.
Step-by-step explanation:
Pine Bluff Middle School's dance committee raises $72 from a bake sale and anticipates $4 for each ticket sold for the Spring Fling dance.
The cost of the dance will be $400.
Let x represent the number of tickets the committee could sell.
The total income amounts to 72 + 4 × x.
After paying for the dance, which costs $400, the committee should have some funds remaining.
This leads to the inequality used to ascertain the number of tickets the committee can sell while ensuring they have money left after the dance expense, formulated as:
72 + 4 × x 400.