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".