The concentration c(t) of a certain drug in the bloodstream after t minutes is given by the formula c(t)=0.04(1−e−0.2t). what is the concentration after 13 minutes? round to three decimal places.

We know the concentration equation of a drug after t minutes, with that, we want to get the concentration after 13 minutes, which is:

c(13) = 0.037

So we know that the equation for the concentration after t minutes is:

We want to get the concentration after 13 minutes, so we just need to evaluate t = 13 in the above equation, we will get:

This is the concentration after 13 minutes.

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0.037

Step-by-step explanation:

The question presents an exponential model linking concentration to the time.

We are supplied with the time here and we are asked to get the value for the concentration. What we simply need to do

Is to make a direct substitution

Thus, the concentration after 13 minis is as follows:

C(t) = 0.04(1 - e-0.2(13))

C(t) = 0.04( 1 - 0.074273578214)

C(t) = 0.04(0.925726421786)

C(t) = 0.037029056871

C(t) = 0.037 to three decimal places

The number of gallons of 100% mixture to be added is 6.11 gallons and the 10% mixture to be added is 48.89 gallons.

Step-by-step explanation:

Let us assume that x gallons of 10% mixture and y gallons of 100% mixture are added to make 55 gallons of 20% mixture.

So, x + y = 55 ............. (1)

And

⇒ 0.1x + y = 0.2x + 0.2y

⇒ 0.1x = 0.8y

⇒ x = 8y ........... (2)

So, from equation (1) we get, 8y + y = 55

⇒ 9y = 55

⇒ y = 6.11 gallons.

Therefore, the number of gallons of 100% mixture to be added is 6.11 gallons and a 10% mixture to be added is (55 - 6.11) = 48.89 gallons. (Answer)