Answer: B) The typical exponential function, y = ax, has asymptote the x-axis and y-intercept x = 0.
Step-by-step explanation:
For the funcion [tex]y = a^x[/tex], the asymptote is the value that the function would never assum, but gets really close. In this case, there is no value for y = 0, because[tex]y = a^x\\0 = a^x \\ln(0) = x.lna\\ln(0)[/tex]is not defined! This way, asymptote is x-axis (y=0).
y-intercept ⇒ x=0, so
[tex]y=a^x\\y=a^0=1[/tex]
This, way, the point (0,1)
alternative b
The typical exponential function y = ax has a horizontal asymptote y = 0 and a y-intercept at the point (0,1), which makes Option B the correct answer.
In this context, the function will approach an asymptote, which is a line that the graph gets infinitely close to without touching. Specifically, for an exponential function, the horizontal asymptote is y = 0 regardless of the value of a, provided that a is nonzero. As the value of x gets very large or very negative, the value of y will get very close to 0 but will never actually reach it.
Additionally, the y-intercept of the function is the point at which it crosses the y-axis. This occurs when x is 0. Substituting 0 for x in the function, we get y = a0, which simplifies to y = 1 because any nonzero number to the power of 0 is 1. Therefore, the y-intercept of the function is (0,1).
So, for the question asking about the asymptote and y-intercept of the typical exponential function y = ax, the correct answer is Option B: asymptote y = 0; y-intercept (0,1).
The hourly operating cost of a certain plane, which seats up to 295 passengers, is estimated to be $3770. If an airline charges each passenger a fare of $100 per hour of flight, find the hourly profit P it earns operating the plane as a function of the number of passengers x ...?
The hourly profit of an airline operating a plane can be calculated by subtracting the operating cost from the revenue earned from passengers.
Explanation:The hourly profit of an airline operating a plane can be expressed as the difference between the revenue earned from passengers and the operating cost of the plane.
The revenue earned from passengers can be calculated by multiplying the fare per passenger by the number of passengers. In this case, the fare is $100 per hour of flight, and the number of passengers is represented by x.
The operating cost of the plane is given as $3770 per hour.
Therefore, the hourly profit P can be expressed as:
P = (fare per passenger) * x - (operating cost of the plane)
Substituting the given values:
P = $100 * x - $3770
SO CONFUSED PLEASE HELP
Which situations can be represented by an exponential function? Select each correct answer.
On the highway, Kareem's car gets 38 mpg.
Shu Fang has $25.75 deducted from her checking account every month.
A toad population is increasing by about 7.5% each year.
An event organizer finds each year's attendance for the past five years is about 4/5 of the previous year's attendance.
Answer: A toad population is increasing by about 7.5% each year.
An event organizer finds each year's attendance for the past five years is about 4/5 of the previous year's attendance.
Step-by-step explanation:
On the highway, Kareem's car gets 38 mpg.
This can be modeled with a linear relationship between the miles and the gallons of fuel needed.
Shu Fang has $25.75 deducted from her checking account every month.
Here we know that each month a constant amount is deducted from her, this is not an exponential relation.
A toad population is increasing by about 7.5% each year.
If the population initially was an amount P, after one year the population is P*1.075, after two years the population is P*(1.075)^2 and so on, this can be modeled with an exponential function where the years variable, the function will have the general form:
Population(y) = P*(1.075)^y
An event organizer finds each year's attendance for the past five years is about 4/5 of the previous year's attendance.
If the first year the population is X, the year after the attendance will be (4/5)X, and the year after this process applies again, so you have a 4/5 of the previous attendance, the attendance now is (4/5)^2*X
This also can be modeled with an exponential function, of the shape:
Attendance (y) = X*(4/5)^y, where again, y means years.
The thing you may notice is that in this case the model only works for the lapse of 5 years that the event organizer said.
a(x+b)=c solve for x
Intersecting chords form a pair of congruent, vertical angles.
A. True
B. False
Answer:
True!
Step-by-step explanation:
What is the surface area of a piece of pipe that is open at both ends, has a radius of 6 inches, and a height of 18 inches? (Use 3.14 for π.)
1/2 x = 20 solve for x
The sum of the perimeters or two different squares is 32 centimeters , and the difference between there perimeters is 8 centimeters. if x represents the side length of the larger square and y represents the side length of the smaller square , Which of the following systems of equations could be used to find the dimensions of the squares?
A. x+y=32
x-y=8
B. 4x+4y=32
4x-4y=8
C. 2x+2y=32
2y-2x=8
D. 2x+2y=32
4x-2y=8
The correct system of equations to find the dimensions of the squares is option A: x + y = 32 and x - y = 8.
Explanation:To find the dimensions of the squares, we can set up a system of equations. Let x represent the side length of the larger square and y represent the side length of the smaller square.
The sum of the perimeters is given as x + y = 32. The difference between the perimeters is given as x - y = 8.
So, the correct system of equations to find the dimensions of the squares is option A: x + y = 32 and x - y = 8.
The correct system of equations to find the dimensions of the squares is x + y = 32 and x - y = 8. Solving this system using the method of elimination gives us the dimensions of the squares: 20 cm for the larger square and 12 cm for the smaller square.
Explanation:The correct system of equations to find the dimensions of the squares is:
x + y = 32
x - y = 8
To solve this system, we can use the method of elimination. Adding the two equations will eliminate the y terms, allowing us to solve for x.
Adding the equations:
x + y + x - y = 32 + 8
2x = 40
x = 20
Substituting the value of x back into one of the original equations, we can solve for y.
Using the equation x + y = 32:
20 + y = 32
y = 12
Therefore, the dimensions of the larger square are 20 cm, and the dimensions of the smaller square are 12 cm.
3(mx)4 + 5 What is the coefficient in the expression? A) x B) 3 C) 4 Eliminate D) 5
Answer:
Step-by-step explanation:
Answer choice is B) 3
Given the function f(x) = x3 + 2x2 − 3x − 5, what is resulting function when f(x) is shifted to the right 1 unit?
Simplify.
1/4+4(1/2−3/4)^2
A population of bacteria is growing according to the function below, where t is in hours. How many hours will it take for the population to grow to 1,000 bacteria? Round your answer to the nearest integer. Do not include units in your answer.
B(t) = 50 e2.5t ...?
Which set is equivalent to (a u b) n c
Lorena deposited $2372 into an account that earns 4.5% interest which is compounded once a year. how much money will lorena have in the account in 20 years?
Answer:
5720.59
Step-by-step explanation:
I know it's correct
How to put 0.258 0.4 0.52 1.25 0,04 from least to greatest?
What is 830% written as a decimal?
8300
83
0.0083
8.3
8.3 i think
Using complete sentences, explain which method you would use to solve the following system of equations and why. In your answer, include the solution to one of the variables and how you found it using the method you chose.
2x + y + z = –7
x – 3y + 4z = –14
x – 2y – 3z = –11
Write two (2) scenarios that describe two different real-world functions. Think of your own variables that are not included in the above list. As you did for the other functions, identify the independent and dependent variables and assign the letters x and y to represent each variable quantity. Then create a set of at least five ordered pairs in (x, y) form with values that make sense for your function.
What is the distance from the origin of point A graphed on the complex plane below?
a. square root of 5
b. square root of 13
c. 9
d. 13
Answer:
Answer is b
Step-by-step explanation:
125 + .375=?
0.654 + 0.389 - 0.293=?
Evaluate 7 + (-3x2) for x = 0.
-2
0
4
7
Answer:7+(-3.0^2)
7+0
7
Step-by-step explanation:
The only part of the United States explored by Russia was the:
A : Hudson River
B : Southwest and Mexico
C : Mississippi River
D : Northwest coastline
Answer:
d
Step-by-step explanation:
d
Dominic, Ralf and Peter have just eaten a HUGE Christmas meal. Dominic now weighs half as much as Ralf, and Peter weighs three times as much as Dominic. Together they weigh 720 pounds. How much does Dominic weigh?
What is the area of a regular octagon with 12 as each side. Round to nearest hundredth.
How many times can 57 go into 413?
Tomorrow, 567 people will want tickets to concert. only 417 tickets are available. how many people will be able to get tickets?
The maximum speed of the Tupolev Tu -144 airliner is 694 m/s. What is this speed in kilometers per hour?
Answer: the correct answer would be 2498.4 km/h
*i got this question correct*
Find the vertex of a function f(x)=-3x^2+9x-15 by completing the square
What is the common difference d of the sequence? −15, −4, 7, 18, 29, ...
Answer:
The common difference is [tex]11[/tex]
Step-by-step explanation:
we know that
In an Arithmetic Sequence the difference between consecutive terms is a constant called the common difference
so
In this problem we have
[tex]-15,-4,7,18,29,...[/tex]
Let
[tex]a1=-15\ a2=-4\ a3=7\ a4=18\ a5=29[/tex]
Find the difference between consecutive terms
[tex]a5-a4=29-18=11[/tex]
[tex]a4-a3=18-7=11[/tex]
[tex]a3-a2=7-(-4)=11[/tex]
[tex]a2-a1=-4-(-15)=11[/tex]
therefore
The sequence is an Arithmetic Sequence
The common difference is [tex]11[/tex]
The sum of two numbers is 10. if one number is subtracted from the other the result is -2. find two numbers
A prime number is always greater than 1 false or truth and why
A prime number must be greater than 1 because by definition, a prime number has exactly two distinct positive divisors: 1 and the number itself. If a number is less than or equal to 1, it cannot be prime.
The statement that a prime number is always greater than 1 is indeed true. A prime number is defined as a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. If a number is less than or equal to 1, it cannot be prime because the prime numbers must be greater than 1 to have at least two distinct positive divisors (1 and the number itself).
For example, the first few prime numbers are 2, 3, 5, 7, 11, and 13. Each of these numbers is greater than 1 and cannot be divided evenly by any number other than 1 and itself. By contrast, the number 1 is not considered a prime because it has only one positive divisor, which is 1 itself. Since primes must have exactly two distinct divisors, 1 does not meet this criterion.