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lions [1.4K]
3 years ago
8

A cooking show currently has about 223,00 regular viewers. The number of regular viewers has been decreasing at a rate of 4.7% p

er year. Which is the best prediction for the number of regular viewers the show will have in 6 years?
35,420
37,167
104,810
167,056
Mathematics
1 answer:
Mazyrski [523]3 years ago
5 0
The best prediction for the number of regular spectators that the program will have in 6 years is obtained with the following formula:
 Pf = Po×(1-b) ^ t
 Where:
 Pf = final population
 Po = initial population
 b = decrease rate
 t = timpo in years
 So:
 Pf = 223.00×(1-0.047) ^ 6
 Pf = 167,056
 The answer is the last option.
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Answer:

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4 years ago
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WITCHER [35]
This problem is half understanding the question and half just plugging in numbers.

Understanding the Question:
So its saying that n = whole number bigger than one, making n = 2, 3, 4, 5, etc.

Now try plugging any number n into the a_n = 4a_{n-1} equation. Let's use 2 to make it simple. If you plug in 2, you get:
a_2 = 4a_{2-1}\\
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Remember that the subscripts (the small numbers in the corner) are simply the term number. a_1 is term 1, a_2 is term 2, etc. The equation is saying that "term 2 = 4 times term 1."

If you keep plugging in random numbers for n, you'll see that the equation basically says, "a term = 4 times the term right before it." That makes it easy to plug and chug to get our answer.

Plugging and Chugging
Now we understand the question is asking for the first 4 terms, and each term is 4 times the last term. You're told that term 1, a_1 = 6. That makes the next four terms:

Term 2
a_2 = 4a_{2-1}\\
 a_2 = 4a_1\\
 a_2 = 4(6)\\
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Term 3
a_3 = 4a_{3-1}\\ a_3 = 4a_2\\ a_3 = 4(24)\\ a_3 = 96

Term 4
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Your first 4 terms are 4, 24, 96, and 384.

--------

Answer: A) F

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4 years ago
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3 years ago
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A triangle has vertices at A(–2, 4), B(–2, 8), and C(6, 4). If A prime has coordinates of (–0. 25, 0. 5) after the triangle has
babunello [35]

The true statements about the dilation are as follows;

The scale factor is One-eighth

The coordinates of the C prime are (0.75, 0.5).

The coordinates of B prime are (–0.25, 1).

Given

A triangle has vertices at A(–2, 4), B(–2, 8), and C(6, 4).

If A prime has coordinates of (–0. 25, 0. 5) after the triangle has been dilated with a center of dilation about the origin.

<h3>What is transformation?</h3>

Transformation is the movement of a point from its initial location to a new location. If an object is transformed then all its points are also transformed. Types of transformation are reflection, dilation, rotation, and translation.

Dilation is the enlargement or reduction in the size of an object. If a point X(x, y)  is dilated about the origin by a factor k, its new location is X'(kx, ky).

Triangle ABC with vertices at A(–2, 4), B(–2, 8), and C(6, 4) is dilated to give A'(-0.25, 0.5)

kA = A'

(-2k, 4k) = (-0.25, 0.5)

-2k = -0.25, hence k = 1/8

Therefore the scale factor is 1/8 (one- eight)

The new location of the vertices is B'(-0.25, 1), C'(0.75, 0.5)

To know more about Transformation click the link given below.

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