What is the total price of a $60 restaurant tab if you leave a 15% tip?
1 answer:
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Note that , so that
is the product of two consecutive integers. This means one of them must be even, and the other is odd. The product of an odd number and an even number is itself an even number, so
for any integer
.
Answer:
10-hour decay factor = 0.13012
5-hour decay factor = 0.52173
1-hour decay factor = 0.87799
154.52624 mg of caffeine
Step-by-step explanation:
Exponential decay is the decrease in a quantity N according to:
where
= initial value of quantity N
N(t) = quantity N at time t
k = decay constant associated to physical properties of N
= decay factor
Substituting the values from the problem:
t = 10 hours
= 0.2722
Then, solving for k:
With the value of the decay constant k, you could calculate the decay factor at any given time. For t = 5 hours, the decay factor is given by:
For t = 1 hour, the decay factor is given by:
If there are 176 mg in Tony's body 1.23 hours after consuming the energy drink, then you could take this value as the initial value of quantity N, i.e. . Then, the quantity of caffeine in Tony's body 2.23 hours later is just the quantity N(t) one hour later from the initial value (1.76 mg), then:
Note that is the 1-hour decay factor previously calculated.