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iragen [17]
1 year ago
7

Topic: Recognizing Linear and Exponential and Quadratic Functions.

Mathematics
1 answer:
BigorU [14]1 year ago
5 0

Answer:

  Recursive: f(1) = 1; f(n) = f(n-1)/3

  Equation: f(x) = 5/3·(1/3)^(x-1)

Step-by-step explanation:

You know this is an exponential function because sequential lines in the table have a common ratio of f(x) values:

  f(2)/f(1) = (5/9)/(5/3) = 3/9 = 1/3

  f(3)/f(2) = (5/27)/(5/9) = 9/27 = 1/3

and it continues like that.

Besides telling you the function is exponential, it also tells you that each term is 1/3 of the previous term.

<h3>Recursive formula</h3>

The value of f(1) is read from the table. For x = 1, that value is ...

  f(1) = 5/3

As we noticed above, each term is 1/3 the previous term, so the recursive relation is ...

  f(n) = (1/3)·f(n-1)

<h3>Equation</h3>

The general form of the equation for a geometric (exponential) relation is ...

  f(x) = f(1)·r^(x-1) . . . . . . where f(1) is the first term, and r is the common ratio

For this function, we have f(1) = 5/3 and r = 1/3, so the equation is ...

  f(x) = 5/3·(1/3)^(x-1)

__

<em>Additional comment</em>

When given values of x that count from 1, we often express the equation in terms of (x-1). That equation can be simplified so the exponent is x.

  f(x) = 5·(1/3)^x

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Write a translation rule that maps point D(7,-3) onto point D'(2,5).
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A rectangle has an area of 20 cm^2. What will the area be if the rectangle tripled in size?
antoniya [11.8K]

Answer:

  180 cm^2

Step-by-step explanation:

For similar figures the ratio of areas is the square of the ratio of linear dimensions.

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4 0
2 years ago
Darin can purchase tile at a store for 0.79 per tile and rent a tile saw for $24. At another store, he can borrow the tile saw f
ankoles [38]
Let us denote the number of tiles by T.

In the first store, if Darin bought T tiles, he would need to spend:
                        0.79\times T+24 (measured in $)

In the second store, if Darin bought T tiles, he would need to spend:
                        1.19\times T (measured in $)

For the cost to be the same at both stores, it means (measured in $)
                                           1.19T=0.79T+24

Moving 0.79T over to the left hand side and changing signs:
                                            1.19T-0.79T=24
                                            0.4T=24
                                            T= \frac{24}{0.4}
                                            T=60 tiles

Let's check. If he buys 60 tiles in the first store, he spends:
                              $0.79×60 + $24 = $47.40 + $24 = $71.40

If he buys 60 tiles in the second store, he spends:
                                               $1.19×60 = $71.40

∴ Darin needs to buy 60 tiles for the cost to be the same at both stores.
7 0
3 years ago
Please help with math
Ivan

Answer:

B is the answer

Step-by-step explanation:

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2 years ago
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