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Verizon [17]
3 years ago
8

Tina asks the question "Does caffeine increase the heart rate of an earthworm?" In Test 1, she measures the heart rate by lookin

g at the earthworm under a microscopes, the earthworm has a heart rate of 50 bpm (beats per minute). In Test 2, she places a few drops of caffeine on the earthworm's skin and measures the rate again. In this test, the heart rate is 68 bpm. The independent variable is
Biology
1 answer:
Greeley [361]3 years ago
7 0
The independent variable is the caffeine.
it controls the bpm.
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The rate at which the concentration of a drug in the bloodstream decreases is proportional to the concentration at any time t. I
Westkost [7]

Answer:

C(t) = C_oe^{-kt}

Explanation:

From the given information:

At any given time (t), let c(t) represent the concentration of the drug present in bloodstream.

Deriving the equation:

\dfrac{dC}{dt} decrease proportionally to Concentration C

i.e

\dfrac{dc}{dt} \alpha - C

\dfrac{dc}{dt} = -k C

\dfrac{dc}{c} = -k dt

\int \dfrac{dc}{c} = -k \int dt

㏑(C) = -kt + λ

where,

λ is the integration constant.

Integrating at t = 0, concentration of blood = Co g/mL

C(0) = Co

㏑(C₀) = 0 + λ

λ = ㏑(C₀)

From ㏑(C) = -kt + λ

㏑(C) = -kt + ㏑C₀

㏑(C)  - ㏑C₀ =  -kt

\dfrac{C}{C_o} = e^{-kt}

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∴

The concentration of drug in blood at any time t is:

C(t) = C_oe^{-kt}

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