Math HW3
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quiz_5.docx
SHORT ANSWER with Work Shown. Record your answers and work.
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1 |
Given the function f, prove that f is one-to-one using the definition of a one-to-one function.
f(x) = 4 2x
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2 |
Graph the equation by substituting and plotting points. Then reflect the graph across the line y = x to obtain the graph of its inverse.
y = x² + 1
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3 |
For the function f, use composition of functions to show that is as given.
f(x) = (x) = 4x 5
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4 |
Find each of the following, to four decimal places, using a calculator.
a) ( ²
b) log 0.082
c) ln 0
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5 |
a) Sketch the graph and use the graph to determine whether the function is one-to-one. b) b) If the function is one-to-one, find a formula for the inverse.
f(x) = 7 x
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6 |
Convert to an exponential equation.
a) t = 7
b) ln 0.38 = 0.9676
c) Q = k
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7 |
Find each of the following. Do not use a calculator.
a)
b) ln e
c) log 1 d) log
e)
f) 4
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8 |
Convert to a logarithmic equation.
a)
b)
c)
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9 |
Graph.
f(x) = ln x
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10 |
The number of foreign nationals who came to the United States to marry an American using a “fiancée Visa” has grown exponentially in recent years. The total number of fiancée visas is given by the function f(x) = 5728.98 ,
Where x is the number of years since 1990 (Source: US Department of Homeland Security).
a) Find the total number of Visas in 2006.
b) Find the total number of Visas in 2009.
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11 |
The value of a stock is given by the function
V(t) = 58 ( 1 ) + 20 ,
Where V is the value of the stock after time t, in months. Find V (1), V (2), V (4), V (6), and V (12).
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12 |
The bacteria Escherichia Coli are commonly found in the human intestines. Suppose that 3,000 of the bacteria are present at time t = 0. Then under certain conditions, t minutes later, the number of bacteria present is
N (t) = 3000
How many bacteria will be present after 10 minutes? 20 minutes? 30 minutes? 40 minutes? And 60 minutes?
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End of Quiz Five |
