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:

f(m)=500((1)/(2))^((m)/( 20)) The function models f, the amount of a particular medicine in milligrams in a patient's bloodstream, m minutes after the medicine is fully absorbed. Based on the function, how many minutes does it take for the amount of medicine in the patient's bloodstream to reduce by half? Choose 1 answer: (A) (1)/(2) (B) 10 (c) 20 (D) 250

f(m)=500(12)m20 f(m)=500\left(\frac{1}{2}\right)^{\frac{m}{20}} \newlineThe function models f f , the amount of a particular medicine in milligrams in a patient's bloodstream, m m minutes after the medicine is fully absorbed. Based on the function, how many minutes does it take for the amount of medicine in the patient's bloodstream to reduce by half?\newlineChoose 11 answer:\newline(A) 12 \frac{1}{2} \newline(B) 10 \mathbf{1 0} \newline(C) 2020\newline(D) 250 \mathbf{2 5 0}

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. f(m)=500(12)m20 f(m)=500\left(\frac{1}{2}\right)^{\frac{m}{20}} \newlineThe function models f f , the amount of a particular medicine in milligrams in a patient's bloodstream, m m minutes after the medicine is fully absorbed. Based on the function, how many minutes does it take for the amount of medicine in the patient's bloodstream to reduce by half?\newlineChoose 11 answer:\newline(A) 12 \frac{1}{2} \newline(B) 10 \mathbf{1 0} \newline(C) 2020\newline(D) 250 \mathbf{2 5 0}
  1. Given function: We are given the function f(m)=500×(12)m20f(m) = 500 \times \left(\frac{1}{2}\right)^{\frac{m}{20}}, which models the amount of medicine in a patient's bloodstream mm minutes after the medicine is fully absorbed. We want to find the value of mm that makes f(m)f(m) half of the initial amount, which is 500500 mg.
  2. Finding half of initial amount: To reduce the amount of medicine by half, we need to find mm such that f(m)=500×(1/2)f(m) = 500 \times (1/2). This means we are looking for when f(m)f(m) equals 250250 mg, since 500×(1/2)=250500 \times (1/2) = 250.
  3. Setting up the equation: Setting up the equation, we have 500×(12)m20=250500 \times \left(\frac{1}{2}\right)^{\frac{m}{20}} = 250. To solve for mm, we can divide both sides of the equation by 500500 to isolate the exponential term.
  4. Simplifying the equation: After dividing by 500500, we get (1/2)(m/20)=250/500(1/2)^{(m/20)} = 250/500, which simplifies to (1/2)(m/20)=1/2(1/2)^{(m/20)} = 1/2.
  5. Setting exponents equal: Since the bases are the same on both sides of the equation, we can set the exponents equal to each other. This gives us m20=1\frac{m}{20} = 1.
  6. Solving for m: Multiplying both sides of the equation by 2020 to solve for mm, we get m=20×1m = 20 \times 1, which simplifies to m=20m = 20.

More problems from Compare linear and exponential growth

Question
Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits xx days to pick up the motorcycle.\newlineWrite an equation for the function. If it is linear, write it in the form g(x)=mx+bg(x) = mx + b. If it is exponential, write it in the form g(x)=a(b)xg(x) = a(b)^x.\newlineg(x)=‾g(x) = \underline{\hspace{3em}}
Get tutor helpright-arrow

Posted 8 months ago

Question
How does f(t)=−2t−7f(t)=-2t-7 change over the interval from t=−7t=-7 to t=−6t=-6?\newlineChoices:\newline[f(t) decreases by 2]\left[\text{f(t) decreases by } 2\right]\newline[f(t) increases by 2]\left[\text{f(t) increases by } 2\right]\newline[f(t) increases by 200%]\left[\text{f(t) increases by } 200\%\right]\newline[f(t) decreases by a factor of 2]\left[\text{f(t) decreases by a factor of } 2\right]
Get tutor helpright-arrow

Posted 8 months ago

Question
How does g(t)=9tg(t)=9^t change over the interval from t=1t=1 to t=3t=3?\newlineChoices: \newline[g(t) decreases by a factor of 81]\left[\text{g(t) decreases by a factor of } 81\right]\newline[g(t) increases by a factor of 81]\left[\text{g(t) increases by a factor of } 81\right]\newline[g(t) increases by 18%]\left[\text{g(t) increases by } 18\%\right]\newline[g(t) decreases by 9%]\left[\text{g(t) decreases by } 9\%\right]
Get tutor helpright-arrow

Posted 8 months ago

Question
Both of these functions grow as xx gets larger and larger. Which function eventually exceeds the other?\newline Choices:\newline(A)f(x)=8x+3.3(A)f(x) = 8x + 3.3\newline(B)g(x)=3.3x−5(B)g(x) = 3.3^x - 5
Get tutor helpright-arrow

Posted 9 months ago

Question
Both of these functions grow as x x gets larger and larger. Which function eventually exceeds the other?\newlineChoices:\newline(A) f(x)=2x+9(A) \ f(x) = 2x + 9 \newline(B) g(x)=2x(B)\ g(x) = 2^x
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions f(x) f(x) and g(x) g(x) are differentiable. \newlineThe function h(x) h(x) is defined as: h(x)=g(x)f(x) h(x)=\frac{g(x)}{f(x)} \newlineIf f(8)=1 f(8)=1 , f′(8)=−6 f'(8)=-6 , g(8)=8 g(8)=8 , and g′(8)=−10 g'(8)=-10 , what is h′(8) h'(8) ? \newlineSimplify any fractions. \newlineh′(8)= h'(8)= ______
Get tutor helpright-arrow

Posted 8 months ago

Question
The functions p(x) p(x) and q(x) q(x) are differentiable. \newlineThe function r(x) r(x) is defined as: r(x)=p(x)q(x) r(x)= \frac{p(x)}{q(x)} \newlineIf p(3)=2 p(3)= 2 , p′(3)=4 p'(3)= 4 , q(3)=6 q(3)= 6 , and q′(3)=9 q'(3)= 9 , what is r′(3) r'(3) ? \newlineSimplify any fractions. \newliner′(3)= r'(3)= _____
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions u(x) u(x) and v(x) v(x) are differentiable. \newlineThe function w(x) w(x) is defined as: w(x)=u(x)v(x) w(x)= \frac{u(x)}{v(x)} \newlineIf u(5)=3 u(5)= 3 , u′(5)=−2 u'(5)= -2 , v(5)=7 v(5)= 7 , and v′(5)=1 v'(5)= 1 , what is w′(5) w'(5) ? \newlineSimplify any fractions. \newlinew′(5)= w'(5)= _____
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions a(x) a(x) and b(x) b(x) are differentiable. \newlineThe function c(x) c(x) is defined as: c(x)=a(x)b(x) c(x)= \frac{a(x)}{b(x)} \newlineIf a(2)=4 a(2)= 4 , a′(2)=5 a'(2)= 5 , b(2)=1 b(2)= 1 , and b′(2)=−3 b'(2)= -3 , what is c′(2) c'(2) ? \newlineSimplify any fractions. \newlinec′(2)= c'(2)= _____
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions m(x) m(x) and n(x) n(x) are differentiable. \newlineThe function o(x) o(x) is defined as: o(x)=m(x)n(x) o(x)= \frac{m(x)}{n(x)} \newlineIf m(7)=2 m(7)= 2 , m′(7)=−1 m'(7)= -1 , n(7)=4 n(7)= 4 , and n′(7)=8 n'(7)= 8 , what is o′(7) o'(7) ? \newlineSimplify any fractions. \newlineo′(7)= o'(7)= _____
Get tutor helpright-arrow

Posted 9 months ago

View all (345)

Related topics

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