The half life of a certain substance is about 4 hours. The graph shows the decay of a 50 gram sample of the substance that is me
asured every hour for 9 hours.
Which function can be used to determine the approximate number of grams of the sample remaining after t hours?
a
y = 50(0.85)x
b
y = 25(0.15)x
c
y = 50(0.15)x
d
y = 25(0.85)x
Which function can be used to determine the approximate number of grams of the sample remaining after t hours?
a
y = 50(0.85)x
b
y = 25(0.15)x
c
y = 50(0.15)x
d
y = 25(0.85)x
2 answers:
I fail to see how those formulas accurately represent exponential decay. (Are you sure those are correct?)
The proper formula to determine the remaining quantity is:
ending amount = Bgng Amount / 2^n
where "n" signifies the number of half-lives that have occurred.
For instance, if the half-life is 4 hours and we're assessing the total after 9 hours (which equals 2.25 half-lives), we would calculate:[[@#TAG_7]]ending amount = Bgng Amount / 2^n
ending amount = 50 / (2^(9/4))
ending amount = 50 / 2^2.25
ending amount = 50 / <span><span><span>4.75682846 </span>
</span></span><span><span>ending amount = </span> 10.5112 grams
</span>This aligns with what we see on the graph.
The proper formula to determine the remaining quantity is:
ending amount = Bgng Amount / 2^n
where "n" signifies the number of half-lives that have occurred.
For instance, if the half-life is 4 hours and we're assessing the total after 9 hours (which equals 2.25 half-lives), we would calculate:[[@#TAG_7]]ending amount = Bgng Amount / 2^n
ending amount = 50 / (2^(9/4))
ending amount = 50 / 2^2.25
ending amount = 50 / <span><span><span>4.75682846 </span>
</span></span><span><span>ending amount = </span> 10.5112 grams
</span>This aligns with what we see on the graph.
Response:
a)
Detailed explanation:
Let's denote the function that appropriately reflects the situation as
where a and b are unknown variables,[[@#TAG_18]]
From the diagram provided,[[@#TAG_20]]
when x = 1, y equals 42.5,[[@#TAG_22]]
------(1)
Again, when x = 4, y is equal to 26,[[@#TAG_30]]
(using equation (1))
Again, with equation (1),
a = 50.0642203646
Consequently, the equation representing the graph is
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