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2 years ago

Which statements are true about exponential decay functions check all that apply

Mathematics

2 answers:

lisabon 2012 [21]2 years ago

5 0

Answer:

The correct statements are:

1) The domain is all real numbers.

4) The base must be less than 1 and greater than 0.

5) The function has a constant multiplicative rate of change.

Step-by-step explanation:

Any function in the form f(x)=ab^x, where a > 0, b > 0 and b not equal to 1 is called an exponential function with base b.

if b>1 then we get a exponential growth function and

We know that a exponential decay function is given as:

f(x)=ab^x with 0<b<1

Hence, the statements that are true about the exponential decay functions are:

1) The domain is all real numbers.

This statement is true since the function is defined for all the real values.

2) As the input increases, the output increases.

This statement is false since from the graph we could check that the exponential decay function decreases with the increasing value of x.

3) The graph is the same as that of an exponential growth function .

The statement is false since the graph of growth function increases with increasing x and is opposite of the decay function.

4) The base must be less than 1 and greater than 0.

This statement is true.

5) The function has a constant multiplicative rate of change.

This option is true.

Since there is a constant multiplicative rate of change (i.e. b)

melomori [17]2 years ago

3 0

This is the concept of exponential functions; The statements that are correct about the exponential decay functions are:
1. The domain is all real number
4. The base must be less than 1 and greater than 0
5. The function has a constant multiplicative rate of change

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We are to show that if X ⊆ Y then (X ∪ Z) ⊆ (Y ∪ Z) for sets X, Y, Z.

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2 years ago

Emily is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Emily will earn $

Hitman42 [59]

Answer:

(6,2)

Step-by-step explanation:

Variable Definitions:

x= the number of commercials

y= the number of movies

Each commercial earns Emily $50, so x commercials would earn her 50x dollars in royalties. Each movie earns Emily $150, so y movies would earn her 150y dollars in royalties. Therefore, the total royalties 50x+150y equals $600:

50x+150y=600

Since Emily's songs were played on 3 times as many commercials as movies, if we multiply 3 by the number of movies, we will get the number of commercials, meaning x equals 3y.

x=3y

Write System of Equations:

50x+150y=600

x=3y

Solve for y in each equation:

1) 50x+150y=600

150y=−50x+600

y=-1/3x+4

2) x=3y

y=1/3x

The x variable represents the number of commercials and the yy variable represents the number of movies. Since the lines intersect at the point (6,2) we can say:

Emily's songs were played on 6 commercials and 2 movies.

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2 years ago

Fabio is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be model

ohaa [14]

Answer:

(2, 11/2)

Step-by-step explanation:

This is a vertical parabola; we know that because x is squared here, while y is not. The standard equation of a vertical parabola with vertex (h,k) is

4p(y-k) = (x-h)^2, where p is the distance between the vertex and the focus. Comparing

4p(y-k) = (x-h)^2 to

10(y-3) = (x-2)^2, we see that 4p = 10. Therefore, p = 10/4 = 5/2, which is the vertical distance between the focus and the vertex.

Since the coordinates of the vertex are easily read from the given equation

(x-2)^2=10(y-3): (h,k) = (2, 3)

all we need to do is to add p (5/2) to the y-coordinate (3);

The focus is at (2, 3 + 5/2), or (2, 11/2).

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2 years ago

What is the value of the product (4 – 2i)(6 + 2i)? 20 – 4i 20 + 16i 28 + 16i 28 – 4i

Darya [45]

(4 – 2i)(6 + 2i)

FOIL

First : 4*6 =24

Outer: 4*2i = 8i

Inner: -2i* 6 = -12i

Last: -2i*2i = -4i^2 =-4(-1) =4

Add together

24+8i-12i+4

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Answer: 28-4i

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2 years ago

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1. which angle is congruent to Angle 1?

Inessa [10]

Part 1) which angle is congruent to Angle 1?

we know that

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therefore

the answer Part 1) is

Angle $5$

Part 2) Which can be used to directly prove that Angle 1 =~ Angle 8?

we know that

Alternate exterior angles are defined as two exterior angles on opposite sides of a transversal which lie on different parallel lines.

in this problem

m∠1=m∠8 -------> by alternate exterior angles theorem

therefore

the answer part 2) is the option

Alternate Exterior Angles Theorem

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we know that

Alternate interior angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal

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m∠4= $42\ degrees$

therefore

the answer Part 3) is

$42\ degrees$

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2 years ago

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