Question

The amount A, in milligrans, of a 10-milligram dose of a drug rernaining in the body after t hours is given by the formula A=10(0.8). Find, to the nearest tenth of an howr, how long it takes for half of the drug dose to be left in the body.

Answer 1

It takes approximately 3.5 hours for half of the drug dose to be left in the body.

Step-by-step explanation:

To find how long it takes for half of the drug dose to be left in the body, we need to solve the equation A = 10(0.8) for t. This equation represents the amount of the drug remaining in the body after t hours, with 10 representing the initial dose and 0.8 being the decay factor. We can rewrite the equation as 5 = 10(0.8)^t and solve for t. Taking the logarithm of both sides, we get log(5) = t * log(0.8). Dividing both sides by log(0.8), we find that t is approximately equal to 3.5 hours.