The table is an exponential function, and the equation that represents this function is
The table is given as:
x F(x)
4 15
5 31
7 127
8 255
Rewrite the table as:
x F(x)
4 16 - 1
5 32 - 1
7 128 - 1
8 256 - 1
Express as a base of 2
x F(x)
4 2⁴ - 1
5 2⁵- 1
7 2⁷ - 1
8 2⁸ - 1
Notice that the function is 1 subtracted from 2 raised to the power of the input.
This is represented as:
Hence, the equation of the table is
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Answer:
Step-by-step explanation:
No. of days of study = 6
Amount of food to use for the 6 days = 72 mm
Given that equal amount of food was used each day, amount used per day =
This would enable us derive a function for the amount of food remaining f(x), which can be expressed as a function of the number of days that have passed, (x).
Thus, we would have:
Let's check if this equation expresses the relation of the function well.
At the end of day 1, if we used, 12mm, we would have 72 - 12 = 60mm of food remaining.
If we replace x in the equation we derived, we would get the same 60mm as the amount of food remaining.
If you try 2, 3, 4, 5 days, you'd get same thing.
At the end of the study, after the 6th day, the food would remain nothing.
Replace 6 for x in the relation function derived, you'd get a value of 0.