If a function f ( x ) has values f ( 4 ) = 6 and f ( 8 ) = 18, use what you have learned about function patterns to find f ( 16 ) = if f ( x ) is: a.) Linear function: f ( 16 ) = b.) Power function: f ( 16 ) = c.) Exponential function: f ( 16 ) = d.) Logarithmic function: f ( 16 ) =
Answers
Answer:
a) f(16) = 42
b) f(16) = 54
c) f(16) = 162
d) f(16) = 30
Step-by-step explanation:
a) y = mx + b ∧ m = (f(8) - f(4))/(8-4) ⇒ m = (18 - 6)/(8 - 4) = 3
b = y - mx = 6 - 3(4) = 6 - 12 = - 6
f(16) = 3(16) - 6 = 42
b) y = kxⁿ ∧ f(4) = 6 = k4ⁿ ∧ f(8) = 18 = k8ⁿ ⇒ 18/6 = (k8ⁿ)/(k4ⁿ) ⇒ 3 = 2ⁿ
n = ㏑(3) / ㏑(2) ⇒ k = y/xⁿ ⇒ k = 6/4ⁿ = 2/3
f(16) = 2/3 × 16ⁿ = 54
c) y = aeᵇˣ ∧ f(4) = 6 = aeᵇ⁴ ∧ f(8) = 18 = aeᵇ⁸ ⇒ 18/6 = (aeᵇ⁸)/(aeᵇ⁴) ⇒ 3 = e⁴ᵇ
b = ㏑(3/4) ∧ a = y / eᵇˣ ⇒ a = 6 / e⁴ᵇ = 2
f(16) = 2eᵇ¹⁶ = 162
d) y = a㏑(bx) ∧ f(4) = 6 = a㏑(b4) ∧ f(8) = 18 = a㏑(b8)
⇒ 18 - 6 = a㏑(b8) - a㏑(b4) ⇒ 12 = a㏑(8b/4b) ⇒ a = 12 / ㏑(2)
f(4) = 6 = a㏑(4b) ⇒ b = (√2)/4
f(16) = a㏑(b16) = 30
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area = 15ft²
Question 2:
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Answers
Answer:
Step-by-step explanation:
Given equation :
To write it's factored form :
⇒
⇒
⇒
⇒
⇒
the factored form of of the expression x³ - 1 is (x - 1)(x² + x + 1).
What are the factors of the expression?
Given the expression in the question:
x³ - 1
To factor the expression x³ - 1, we use the difference of cubes formula.
It states that:
a³ - b³ can be factored as (a - b)(a² + ab + b²).
x³ - 1
First, rewrite the expression as:
x³ - 1²
Here, we identify 'a' as x and 'b' as 1.
Applying the difference of cubes formula, we get:
a³ - b³ = (a - b)(a² + ab + b²)
x³ - 1² = ( x - 1)(x² + x + 1²)
Simplify:
x³ - 1² = ( x - 1)(x² + x + 1)
Therefore, the factored form is ( x - 1)(x² + x + 1).
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Answers
the answer is 37-10=27/3=9
Answer:
7
Step-by-step explanation:
The Wilsons have triplets and another child who is 15. Since their ages all add up to 36, we can first start off with subtracting 15 from 36.
36 - 15 = 21
Now we can divide the amount we have from the rest amount of kids, since they are triplets, they are 3:
21 / 3 =
7
Answers
If the researcher set up two rooms—one with a faint rose smell, and one with a faint lemon smell. each participant was asked to enter each room and identify the smell in the room. The research method that the researcher use , and what outcome would be found is: Cross-sectional. The outcome is: As people grow older their sense of smell decrease.
A cross-sectional is a research that is carried out by collecting data from different group of population or by drawing a random sample from a group of population in which the researcher will then study or observe the data collected at a particular period of time.
Based on the given information the researcher is making use of Cross-sectional research method as the researcher what to know how people perceive smell based on their age or how age determine people sense of smell.
The outcome that could be found based on the research is that as people age or grow older their sense of smell decrease or begins to decrease, which simply means that younger people have strongest sense of smell than older people.
Inconclusion If the researcher set up two rooms—one with a faint rose smell, and one with a faint lemon smell. each participant was asked to enter each room and identify the smell in the room. The research method that the researcher use , and what outcome would be found is: Cross-sectional. The outcome is: As people grow older their sense of smell decrease.
Learn more about Cross-sectional here:
Final answer:
The researcher used an experimental method with the type of smell as the independent variable and the identification of the smell as the dependent variable. The outcome would likely reveal differences in odor identification across age groups, with younger ones performing better due to age-related sensory changes.
Explanation:
The research method used in the scenario is known as an experimental method. This technique is adopted in studies where one or more variables are manipulated to analyze the effect on an outcome variable. Here, the independent variable being the type of smell (rose or lemon), and the dependent variable is the identification of the smell. In this experiment, different age groups function as the control variable.
The outcome of the experiment would ideally determine if there's a difference in odor identification across different age groups, and whether the type of scent (rose or lemon) impacts the ability to recognize the odor. Given the information related to sensory changes across different ages found particularly in the sense of smell, it can be postulated that the younger age groups might perform better in identifying the smells correctly. Studies have noted that sense of smell tends to decline after the age of 50.
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