After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is modeled by the function c(t) = 4(e−0.4t − e−0.6t) where the time t is measured in hours and c is measured in µg/ml. what is the maximum concentration of the antibiotic during the first 12 hours? (round your answer to four decimal places.)

The concentration of the antibiotic after 12 hours is 0.0299 µg/ml.

Antibiotics are drugs that are taken to combat diverse bacterial infections. There are several antibiotics on sale and they are used for diseases such as typhoid fever, cholera, pneumonia, etc.

Following the model of the function, we have;

c(t) = 4(e−0.4t − e−0.6t), the concentration of the drug is a function of time.

At time = 12 hours, we have;

c(t) = 4(e−0.4(12) − e−0.6(12))

c(t) = 4(8.2297 × 10^-3 - 0.7466  × 10^-3)

c(t) = 0.0299 µg/ml

Learn more: link

The maximum concentration of the antibiotic during the first 12 hours will be of 0.5926 µg/ml.

Explanation:

The maximum concentration will be at the instant of time in which , and this concentration will be .

So

Applying ln to both sides

The maximum concentration will happens at the time 2.027h, and it will be

The maximum concentration of the antibiotic during the first 12 hours will be of 0.5926 µg/ml.

this disease is :

* endemic (present in a defined area that is a village)

* a bacterial infection (treated with antibiotic)

* communicable by contact (by the hands)

manu-porterage is the most common mode of transmission, it transmits germs from one individual to another via the hands. this concerns infections of exogenous origin.

endemic disease, or endemic disease, refers to a disease that is constantly present in a given population, often tied to a specific geographic origin, as opposed to a pandemic that is not a sporadic disease.

antibiotics are molecules that have the property of killing (bactericidal) or limiting the spread (bacteriostatic) of bacteria.

if you think your dog may have been exposed to a toxin, the best thing to do is to check the label of the item you think your pet ingested. read the information about toxicity. often, but not always, the information on packaging regarding children is relevant to dogs and some manufacturers even discuss dog toxicity. if there is an 800 number on the package – call them! it’s also recommended that you call your veterinarian to confirm the recommendations. if you go to your veterinarian, take all packaging and any information you have on the product.