Mathematics, 05.05.2020 19:16 gd9075

When a certain prescription drug is taken orally by an adult, the amount of the drug (in mg/L) in the bloodstream at t hours is given by the function y=f(t)
1. What is the concentration of the drug in the bloodstream at t= 8 hours?
2. During what time interval is the drug level in the bloodstream increasing? Decreasing?

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Answer from: lays20001

(1) The concentration of drug in the bloodstream in 8 hours is given by

$\rm \bold{y = f (8)}$

(2) The time interval for which $\rm y'=f'(t)0$ the drug level of the bloodstream is increasing.

The time interval for which $\rm y' = f'(t)$ the drug level of the bloodstream is decreasing.

When a certain prescription drug is taken orally by an adult.

the amount of the drug (in mg/L) in the bloodstream at t hours is given by the function y=f(t)

To be determined

(1) The concentration of the drug in the bloodstream at t= 8 hours

(2) During what time interval is the drug level in the bloodstream increasing or deceasing

The amount of the drug (in mg/L) in the bloodstream at t hours is given by the function

y=f(t).......(1)

(1) The concentration of drug in the bloodstream in 8 hours is given by putting t= 8 in the equation (1) which can be formulated as below

$\rm y = f (8)$

(2) From the definition of increasing and decreasing function we can write that

$\rm y = f(x) \; is \; increasing \; when \; f' (x)0 \\and\; y = f(x) ; is \; decreasing \; when \; f' (x)$

By the definition of increasing and decreasing function we can say that

The time interval for which $\rm y'=f'(t)0$ the drug level of the bloodstream is increasing.

The time interval for which $\rm y'=f'(t)$ the drug level of the blood stream is decreasing.

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Answer from: vkffgj

1. y = f(8)

2. So for t which f'(t) > 0, the drug level in the bloodstream is increasing. And for t which f'(t) < 0, it is decreasing.

Step-by-step explanation:

The concentration of the drug in the bloodstream at t hours is:

y = f(t)

1. What is the concentration of the drug in the bloodstream at t= 8 hours?

At t hours, y = f(t)

So at 8 hours, y = f(8)

2. During what time interval is the drug level in the bloodstream increasing? Decreasing?

A function f(t) is increasing when

f'(t) > 0

And is decreasing when

f'(t) < 0

So for t which f'(t) > 0, the drug level in the bloodstream is increasing. And for t which f'(t) < 0, it is decreasing.

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