Mathematics, 22.10.2019 04:00 michaelbernbenn5740

50.the amount of caffeine in a patient’s bloodstream decreases by half every 3.5 hours. a latte contains 150 mg of caffeine, which is absorbed into the bloodstream almost immediately.
b. do you have enough information to find a model that is appropriate for this situation? either find a model or
explain what other information you would need to do so.

Answers: 1

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We have the initial amount of caffeine and the time it takes for it to decrease to half. This is enough information to say that an exponential model is appropriate for this situation.

$C(t) = C(0)e^{-0.197t}$

Step-by-step explanation:

We have the initial amount of caffeine and the time it takes for it to decrease to half. This is enough information to say that an exponential model is appropriate for this situation.

This situation can be modeled by the following equation:

$C(t) = C(0)e^{rt}$

In which C(t) is the ammount of caffeine in the blood at time t, C(0) is the initial amount and r is the rate that it decreases.

The problem states that

A latte contains 150 mg of caffeine, which is absorbed into the bloodstream almost immediately, so C(0) = 150 .

The amount of caffeine in a patient’s bloodstream decreases by half every 3.5 hours, so C(3.5) = 0.5C(0) = 0.5(150) = 75 .

With these informations, we can find the value of r in the equation of the model.

$C(t) = C(0)e^{rt}$

$C(3.5) = C(0)e^{3.5r}$

$75 = 150e^{3.5r}$

$e^{3.5r} = 0.5$

To find the value of r, we can apply ln to both sides of the equation:

$\ln{e^{3.5r}} = \ln{0.5}$

3.5r = -0.69

r = -0.197

So, the model is:

$C(t) = C(0)e^{-0.197t}$

Answer from: Quest

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.

Answer from: Quest

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m= $\frac{b}{a}$ (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m= $\frac{-12}{20}$

m= $\frac{-3}{5}$

putting the value of a,b and m in equation (i) gives us

-12 = $\frac{-3}{5} *20$ + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.

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