Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

An IV administers medication to a patient's bloodstream at a rate of 3 cubic centimeters per hour. At the same time, the patient's organs remove the medication from the patient's bloodstream at a rate proportional to the current volume V of medication in the bloodstream. Which equation describes this relationship? Choose 1 answer: (A) (dV)/(dt)=3-kV B) (dV)/(dt)=-3kV (C) (dV)/(dt)=3k-V (D) (dV)/(dt)=k-3V

An IV administers medication to a patient's bloodstream at a rate of 33 cubic centimeters per hour.\newlineAt the same time, the patient's organs remove the medication from the patient's bloodstream at a rate proportional to the current volume V V of medication in the bloodstream.\newlineWhich equation describes this relationship?\newlineChoose 11 answer:\newline(A) dVdt=3−kV \frac{d V}{d t}=3-k V \newlineB) dVdt=−3kV \frac{d V}{d t}=-3 k V \newline(C) dVdt=3k−V \frac{d V}{d t}=3 k-V \newline(D) dVdt=k−3V \frac{d V}{d t}=k-3 V

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Compare linear and exponential growthright chevron icon

Full solution

Q. An IV administers medication to a patient's bloodstream at a rate of 33 cubic centimeters per hour.\newlineAt the same time, the patient's organs remove the medication from the patient's bloodstream at a rate proportional to the current volume V V of medication in the bloodstream.\newlineWhich equation describes this relationship?\newlineChoose 11 answer:\newline(A) dVdt=3−kV \frac{d V}{d t}=3-k V \newlineB) dVdt=−3kV \frac{d V}{d t}=-3 k V \newline(C) dVdt=3k−V \frac{d V}{d t}=3 k-V \newline(D) dVdt=k−3V \frac{d V}{d t}=k-3 V
  1. Understand the problem: Understand the problem.\newlineThe IV administers medication at a constant rate of 33 cubic centimeters per hour. At the same time, the patient's organs are removing the medication at a rate proportional to the current volume of medication in the bloodstream. We need to find the differential equation that represents this situation.
  2. Identify terms: Identify the terms of the differential equation.\newlineThe rate of change of the volume of medication in the bloodstream over time, dVdt\frac{dV}{dt}, is affected by two factors: the constant rate of administration and the rate of removal, which is proportional to the volume VV.
  3. Formulate equation: Formulate the differential equation.\newlineThe rate of administration is a constant 33 cubic centimeters per hour, so it is a positive term in the equation. The rate of removal is proportional to the volume VV, which means it should be represented as kVkV, where kk is the proportionality constant. Since the medication is being removed, this term should be negative. Therefore, the differential equation should have the form dVdt=\frac{dV}{dt} = administration rate −- removal rate.
  4. Write equation: Write down the differential equation.\newlineThe differential equation that represents the situation is dVdt=3−kV\frac{dV}{dt} = 3 - kV, where 33 represents the constant rate of medication administration and kVkV represents the rate of medication removal.
  5. Match with choices: Match the differential equation with the given choices.\newlineThe correct differential equation is dVdt=3−kV\frac{dV}{dt} = 3 - kV. This matches with choice (A) dVdt=3−kV\frac{dV}{dt} = 3 - kV.

More problems from Compare linear and exponential growth

Question
We want to factor the following expression:\newlinex4+10x+25 x^{4}+10 x+25 \newlineWhich pattern can we use to factor the expression?\newlineU U and V V are either constant integers or single-variable expressions.\newlineChoose 11 answer:\newline(A) (U+V)2 (U+V)^{2} or (U−V)2 (U-V)^{2} \newline(B) (U+V)(U−V) (U+V)(U-V) \newline(C) We can't use any of the patterns.
Get tutor helpright-arrow

Posted 10 months ago

Question
We want to factor the following expression:\newline(x−2)4−(y+3)4 (x-2)^{4}-(y+3)^{4} \newlineWhich pattern can we use to factor the expression?\newlineU U and V V are either constant integers or single-variable expressions.\newlineChoose 11 answer:\newline(A) (U+V)2 (U+V)^{2} or (U−V)2 (U-V)^{2} \newline(B) (U+V)(U−V) (U+V)(U-V) \newline(C) We can't use any of the patterns.
Get tutor helpright-arrow

Posted 10 months ago

Question
We want to factor the following expression:\newline(x−1)2+(x−1)+4 (x-1)^{2}+(x-1)+4 \newlineWhich pattern can we use to factor the expression?\newlineU U and V V are either constant integers or single-variable expressions.\newlineChoose 11 answer:\newline(A) (U+V)2 (U+V)^{2} or (U−V)2 (U-V)^{2} \newline(B) (U+V)(U−V) (U+V)(U-V) \newline(C) We can't use any of the patterns.
Get tutor helpright-arrow

Posted 10 months ago

Question
We want to factor the following expression:\newline9x4+4y2 9 x^{4}+4 y^{2} \newlineWhich pattern can we use to factor the expression?\newlineU U and V V are either constant integers or single-variable expressions.\newlineChoose 11 answer:\newline(A) (U+V)2 (U+V)^{2} or (U−V)2 (U-V)^{2} \newline(B) (U+V)(U−V) (U+V)(U-V) \newline(C) We can't use any of the patterns.
Get tutor helpright-arrow

Posted 10 months ago

Question
We want to factor the following expression:\newline16x4−25 16 x^{4}-25 \newlineWhich pattern can we use to factor the expression?\newlineU U and V V are either constant integers or single-variable expressions.\newlineChoose 11 answer:\newline(A) (U+V)2 (U+V)^{2} or (U−V)2 (U-V)^{2} \newline(B) (U+V)(U−V) (U+V)(U-V) \newline(C) We can't use any of the patterns.
Get tutor helpright-arrow

Posted 10 months ago

Question
We want to factor the following expression:\newlinex4+3x2y+9y2 x^{4}+3 x^{2} y+9 y^{2} \newlineWhich pattern can we use to factor the expression?\newlineU U and V V are either constant integers or single-variable expressions.\newlineChoose 11 answer:\newline(A) (U+V)2 (U+V)^{2} or (U−V)2 (U-V)^{2} \newline(B) (U+V)(U−V) (U+V)(U-V) \newline(C) We can't use any of the patterns.
Get tutor helpright-arrow

Posted 10 months ago

Question
We want to factor the following expression:\newline(x+5)4+2(x+5)2−1 (x+5)^{4}+2(x+5)^{2}-1 \newlineWhich pattern can we use to factor the expression?\newlineU U and V V are either constant integers or single-variable expressions.\newlineChoose 11 answer:\newline(A) (U+V)2 (U+V)^{2} or (U−V)2 (U-V)^{2} \newline(B) (U+V)(U−V) (U+V)(U-V) \newline(C) We can't use any of the patterns.
Get tutor helpright-arrow

Posted 10 months ago

Question
We want to factor the following expression:\newline(x−3)2−10(x−3)+25 (x-3)^{2}-10(x-3)+25 \newlineWhich pattern can we use to factor the expression?\newlineU U and V V are either constant integers or single-variable expressions.\newlineChoose 11 answer:\newline(A) (U+V)2 (U+V)^{2} or (U−V)2 (U-V)^{2} \newline(B) (U+V)(U−V) (U+V)(U-V) \newline(C) We can't use any of the patterns.
Get tutor helpright-arrow

Posted 10 months ago

Question
We want to factor the following expression:\newline(x+7)2+2y(x+7)+y2 (x+7)^{2}+2 y(x+7)+y^{2} \newlineWhich pattern can we use to factor the expression?\newlineU U and V V are either constant integers or single-variable expressions.\newlineChoose 11 answer:\newline(A) (U+V)2 (U+V)^{2} or (U−V)2 (U-V)^{2} \newline(B) (U+V)(U−V) (U+V)(U-V) \newline(C) We can't use any of the patterns.
Get tutor helpright-arrow

Posted 10 months ago

Question
We want to factor the following expression:\newline9x6+6x3y+y2 9 x^{6}+6 x^{3} y+y^{2} \newlineWhich pattern can we use to factor the expression?\newlineU U and V V are either constant integers or single-variable expressions.\newlineChoose 11 answer:\newline(A) (U+V)2 (U+V)^{2} or (U−V)2 (U-V)^{2} \newline(B) (U+V)(U−V) (U+V)(U-V) \newline(C) We can't use any of the patterns.
Get tutor helpright-arrow

Posted 10 months ago

View all (27)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant