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PLS HELP ME

The function f(x) = -3(2)²+¹ +90 represents the number of tokens a child has x hours after arriving at an arcade.
What is the practical domain and range of the function?
Enter your answer by filling in the boxes to correctly complete the statements. If necessary, round to the nearest hundrea
The practical domain of the situation is x
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The practical range of the situation is 90
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PLS HELP ME The function f(x) = -3(2)²+¹ +90 represents the number of tokens a child-example-1
User Larryq
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1 Answer

1 vote

Answer:

  • Practical domain: 0 ≤ x ≤ 3.907
  • Practical Range: 0 ≤ y ≤ 84 where y is an integer, so we have the set {0,1,2,...,83,84}

The 3.907 is approximate.

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Step-by-step explanation:

x = number of hours that elapse

y = f(x) = number of tokens

If we use a graphing tool like a TI84 or GeoGebra, then the approximate solution to -3(2)^(x+1) + 90 = 0 is roughly x = 3.907

At around 3.907 hours is when the number of tokens is y = 0. Therefore, this is the approximate upper limit for the domain. The lower limit is x = 0.

The domain spans from x = 0 to roughly x = 3.907, and we shorten that down to 0 ≤ x ≤ 3.907

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Plug in x = 0 to find y = 84. This is the largest value in the range.

The smallest value is y = 0.

The range spans from y = 0 to y = 84, so we get 0 ≤ y ≤ 84

Keep in mind y is the number of tokens. A fractional amount of tokens does not make sense, so we must have y be a whole number 1,2,3,...,83,84.

The x value can be fractional because 3.907 hours for instance is valid.

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Extra info:

  • The function is decreasing. It goes downhill when moving to the right.
  • The points (0,84) and (1,78) and (2,66) and (3,42) are on this exponential curve.
  • A point like (2,66) means x = 2 and y = 66. It indicates: "after 2 hours, they will have 66 tokens remaining".
User Sam Basu
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8.4k points