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Assoli18 [71]
3 years ago
6

Which statements are true about exponential decay functions? Check all that apply. The domain is all real numbers. As the input

increases, the output increases. The graph is the same as that of an exponential growth function. The base must be less than 1 and greater than 0. The function has a constant multiplicative rate of change.
Mathematics
2 answers:
lorasvet [3.4K]3 years ago
8 0
<h2>Answer:</h2>

The correct options are:

  • The domain is all real numbers.
  • The base must be less than 1 and greater than 0.
  • The function has a constant multiplicative rate of change.
<h2>Step-by-step explanation:</h2>

We know that the exponential function is given by:

                f(x)=ab^x

where a>0 and b are constants.

Also, it represents a growth function if b>1

and a decay function if 0<b<1

where b is the base.

  • x belongs to whole of the real numbers( since the exponential function is well defined for all the real values of x.

Hence, the domain of the function is all the real numbers )

  • Also, the graph of a decay function decreases continuously i.e. with the increasing input value the output value decreases.
  • The exponential decay function always have a constant multiplicative rate of change i.e. b.
bezimeni [28]3 years ago
4 0

Answer:

A D E

Step-by-step explanation:

Edge2020

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Ingrid makes quilts in designs that follow a specific pattern. The first three designs are shown. In designs, the white blocks r
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The number of white and grey blocks in the quilts follows a sequence given by the Design number of the quilt

The numbers and patterns of the blocks are;

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  • The height of the outer grey blocks is 2 blocks more than the Design number, while their rows are 3 blocks more than the Design number

b. The function is \underline{p(n) = n \cdot (n + 1)}

c. The function is \underline{b(n) = (n + 2) \cdot (n + 3) -  n \cdot (n + 1)}}

d.  \underline{t(n) = (n + 2) \cdot (n + 3)  = b(n) - p(n) }

e. The design chosen is <u>Design 9</u>

The number of blocks is <u>132 blocks</u>

Reasons:

The pattern of the design are;

a. The column height of the grey blocks = 2 blocks more than the column height of the white blocks

Width of the outer grey blocks = 2 blocks more than the width of the inner white blocks

The number of white blocks in a design, <em>n</em> is the product of <em>n</em> and (n + 1)

The number of grey blocks in a design <em>n</em>, is the product of (n + 2) and (n + 3) less the number of white blocks in the design

b. Based on the above, the function that represent the number of picture blocks in Design <em>n</em>, is therefore;

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c. Based on the above, the function that represent the number of border blocks in Design <em>n</em>, is therefore;

  • b(n) = (n + 2)·(n + 3) - n·(n + 1)

d. The total number of blocks, t(n) = (n + 2)·(n + 3)

t(n) = (n + 2)·(n + 3) - n·(n + 1) + n·(n + 1)

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e. The given number of picture blocks = 90

The number of picture blocks in a design, n = n × (n + 1)

Therefore, given that the number of picture blocks is 90, we have;

90 = n × (n + 1)

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(n + 10)·(n - 9) = 0

n = 9, or n = -10

Therefore, the design museum chooses is <u>Design 9</u>

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Total blocks in the design the art museum choses, t(9), is given as follows;

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<u />

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