5.7 Chapter Test
Chapter
Chapter 5
Section
5.7
Solutions 19 Videos

Which of the following if the derivative of  y = 5^x?

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Q1

What is the value of lm(e^{-2x}) when  x= 2?

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Q2

What is the derivative of f(x) = e^{-x}\cos x?

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Q3

What is the solution to 50 = 25e^{-2x}?

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Q4

Differentiate each function.

 y = -2e^{\dfrac{-1}{2}x}

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Q5a

Differentiate each function.

 f(x) = x^3e^{2x} - x^2e^{-2x}

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Q5b

Determine the coordinates of any local extrema of the function  y = x^2(e^{-2x}) and classify each as either a local maximum or local minimum.

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Q6

An influenza virus is spreading according to the function P(t) = 50(2)^{\dfrac{t}{2}}, where P is the number of people infected after t days.

a) How many people had the virus initially?

b) How many will be infected in 1 week?

c) How fast will the virus be spreading at the end of 1 week?

d) How long will it take until 1000 people are infected?

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Q7

a) Graph  f(x) = -2e^x and its inverse on the same grid.

b) Identify the key features of both graphs in part a).

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Q8

Determine the equation of the line that is tangent to  f(x) = -2e^x when  x= ln2.

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Q9

A sample of uranium-239 (U-239) decays into neptunium-239 (Np-239) according to the standard decay function  N(t) = N_0 e^{-\lambda t}. After 10 min, the sample has decayed to 64% of its initial amount.

a) Determine the value of the disintegration constant, \lambda .

b) Determine the half-life of U-239.

c) Write the equation that gives the amount of U-239 remaining as a function of time, in terms of its half-life.

d) Suppose the initial sample had a mass of 25mg. How fast is the sample decaying after 15 min?

A pulse in a spring can be modelled with the relation \displaystyle A(x)=15 e^{-x^{2}} , where \displaystyle A  is the amplitude of the pulse, in centimetres. How fast is the amplitude changing when \displaystyle x=1 \mathrm{~cm}  ?