Toxins in pesticides can get into the food chain and accumulate in the body. A person consumes 12 micrograms a day of a toxin, ingested throughout the day. The toxin leaves the body at a continuous rate of 3% every day. Write a differential equation for the amount of toxin, A, in micrograms, in the person's body as a function of the number of days, t.

Question

Mathematics

Brenda Roberts

7 February, 10:10

Toxins in pesticides can get into the food chain and accumulate in the body. A person consumes 12 micrograms a day of a toxin, ingested throughout the day. The toxin leaves the body at a continuous rate of 3% every day. Write a differential equation for the amount of toxin, A, in micrograms, in the person's body as a function of the number of days, t.

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Jace Ferguson · Answer 1

dA/dt = 12 - 0.03A.

Step-by-step explanation:

The rate at which the toxin is taken in or ingested throughout the day Increases by 12 micrograms a day.

The rate at which the toxin is taken out throughout the day decrease by 3 percent that is 0.03.

The differential equation for the amount of toxin, A, in micrograms, in the person's body as a function of the number of days, t = dA/dt.

The rate at which the toxin is taken in or ingested makes dA/dt more positive.

The rate at which the toxin is taken out throughout the day makes dA/dt more negative.

Therefore, dA/dt = (rate at which the toxin is taken in or ingested) - (The rate at which the toxin is taken out throughout the day).

Hence, dA/dt = 12 - 0.03A