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satela [25.4K]
3 years ago
6

A patient is given a 50 mg dose of medicine the medicines effectiveness decreases every hour at a constant rate of 40% what is t

he exponential decay function that models this scenario how much medicine will be left in the patient's system after two hours
Mathematics
2 answers:
Natalija [7]3 years ago
8 0
Exponential decay formula is
y = a(1 - r)^{x}  \\ y = 50(1 - .40) ^{x}
x= hours past
y = 50(1 - .40)^{2}  \\ y = 18
after 2 hours, there are 18 mg of medicine left
prisoha [69]3 years ago
3 0

Answer:

A=50(0.6)^x

18 mg of medicine will be left in the patient's system after two hours.

Step-by-step explanation:

Given,

The initial quantity of the medicine, P = 50 mg,

Also, it decreases every hour at a constant rate of 40%

That is, r = 40 %,

Thus, the quantity of the medicine after x hours,

A=P(1-\frac{r}{100})^r

=50(1-\frac{40}{100})^x

=50(1-0.4)^x

=50(0.6)^x

Which is the required exponential decay function that models this scenario.

The quantity of the medicine after 2 hours,

A=50(0.6)^2=18\text{ mg}

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