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Solve. -How long will it take for $3700\$ 3700 to grow to $34,300\$ 34,300 at an interest rate of 10.3%10.3 \% if the interest is compounded continuously? Round the number of years to the nearest hundredth.


A) 0.22yr0.22 \mathrm { yr }
B) 2.16yr2.16 \mathrm { yr }
C) 2161.95yr2161.95 \mathrm { yr }
D) 21.62yr21.62 \mathrm { yr }

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Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic logarithmic function. - f(x) =log⁡4(x+5) f(x) =\log _{4}(x+5) Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic logarithmic function. - f(x) =\log _{4}(x+5) A) Shift y = \log _ { 4 } x left 5 units B) Shift y = \log _ { 4 } x left 5 units C) Shift y = \log _ { 4 } x right 5 units D) Shift y = \log _ { 4 } x right 5 units


A) Shift y=log⁡4xy = \log _ { 4 } x left 5 units
Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic logarithmic function. - f(x) =\log _{4}(x+5) A) Shift y = \log _ { 4 } x left 5 units B) Shift y = \log _ { 4 } x left 5 units C) Shift y = \log _ { 4 } x right 5 units D) Shift y = \log _ { 4 } x right 5 units
B) Shift y=log⁡4xy = \log _ { 4 } x left 5 units
Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic logarithmic function. - f(x) =\log _{4}(x+5) A) Shift y = \log _ { 4 } x left 5 units B) Shift y = \log _ { 4 } x left 5 units C) Shift y = \log _ { 4 } x right 5 units D) Shift y = \log _ { 4 } x right 5 units
C) Shift y=log⁡4xy = \log _ { 4 } x right 5 units
Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic logarithmic function. - f(x) =\log _{4}(x+5) A) Shift y = \log _ { 4 } x left 5 units B) Shift y = \log _ { 4 } x left 5 units C) Shift y = \log _ { 4 } x right 5 units D) Shift y = \log _ { 4 } x right 5 units
D) Shift y=log⁡4xy = \log _ { 4 } x right 5 units
Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic logarithmic function. - f(x) =\log _{4}(x+5) A) Shift y = \log _ { 4 } x left 5 units B) Shift y = \log _ { 4 } x left 5 units C) Shift y = \log _ { 4 } x right 5 units D) Shift y = \log _ { 4 } x right 5 units

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Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic exponential function. - f(x) =2(x−3) f(x) =2(x-3) Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic exponential function. - f(x) =2(x-3) A) Shift y = 2 ^ { x } left 3 unit(s) B) Shift y = 2 ^ { x } right 3 unit(s) C) Shift y = 2 ^ { x } down 3 unit(s) D) Shift y = 2 ^ { x } up 3 unit(s)


A) Shift y=2xy = 2 ^ { x } left 3 unit(s)
Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic exponential function. - f(x) =2(x-3) A) Shift y = 2 ^ { x } left 3 unit(s) B) Shift y = 2 ^ { x } right 3 unit(s) C) Shift y = 2 ^ { x } down 3 unit(s) D) Shift y = 2 ^ { x } up 3 unit(s)
B) Shift y=2xy = 2 ^ { x } right 3 unit(s)
Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic exponential function. - f(x) =2(x-3) A) Shift y = 2 ^ { x } left 3 unit(s) B) Shift y = 2 ^ { x } right 3 unit(s) C) Shift y = 2 ^ { x } down 3 unit(s) D) Shift y = 2 ^ { x } up 3 unit(s)
C) Shift y=2xy = 2 ^ { x } down 3 unit(s)
Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic exponential function. - f(x) =2(x-3) A) Shift y = 2 ^ { x } left 3 unit(s) B) Shift y = 2 ^ { x } right 3 unit(s) C) Shift y = 2 ^ { x } down 3 unit(s) D) Shift y = 2 ^ { x } up 3 unit(s)
D) Shift y=2xy = 2 ^ { x } up 3 unit(s)
Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic exponential function. - f(x) =2(x-3) A) Shift y = 2 ^ { x } left 3 unit(s) B) Shift y = 2 ^ { x } right 3 unit(s) C) Shift y = 2 ^ { x } down 3 unit(s) D) Shift y = 2 ^ { x } up 3 unit(s)

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Solve the problem. -An initial investment of $14,000 is appreciated for 4 years in an account that earns 13% interest, compounded semiannually. Find the amount of money in the account at the end of the period.


A) $22,826.63
B) $23,169.94
C) $9169.94
D) $21,755.81

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For the function f, use composition of functions to show that f f−1 is as given. \mathrm { f } ^ { - 1 } \text { is as given. } - f(x)=74x,f−1(x)=47xf ( x ) = \frac { 7 } { 4 } x , f ^ { - 1 } ( x ) = \frac { 4 } { 7 } x

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Express as a difference of logarithms. - log⁡4911\log _ { 4 } \frac { 9 } { 11 }


A) log⁡49÷log⁡411\log _ { 4 } 9 \div \log _ { 4 } 11
B) log⁡49−log⁡411\log _ { 4 } 9 - \log _ { 4 } 11
C) log⁡411−log⁡49\log _ { 4 } 11 - \log _ { 4 } 9
D) log⁡29−log⁡211\log _ { 2 } 9 - \log _ { 2 } 11

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Choose the function that might be used as a model for the data in the scatter plot. - Choose the function that might be used as a model for the data in the scatter plot. - A) Polynomial, not quadratic B) Exponential, \mathrm { f } ( \mathrm { x } ) = a \mathrm {~b} ^ { \mathrm { x } } or \mathrm { f } ( \mathrm { x } ) = \mathrm { P } _ { 0 } \mathrm { e } ^ { \mathrm { kx } } , \mathrm { k } > 0 C) Logistic, f ( x ) = \frac { a } { 1 + b e ^ { - k x } } D) Logarithmic, f ( x ) = a + b \ln x


A) Polynomial, not quadratic
B) Exponential, f(x) =a bx\mathrm { f } ( \mathrm { x } ) = a \mathrm {~b} ^ { \mathrm { x } } or f(x) =P0ekx,k>0\mathrm { f } ( \mathrm { x } ) = \mathrm { P } _ { 0 } \mathrm { e } ^ { \mathrm { kx } } , \mathrm { k } > 0
C) Logistic, f(x) =a1+be−kxf ( x ) = \frac { a } { 1 + b e ^ { - k x } }
D) Logarithmic, f(x) =a+bln⁡xf ( x ) = a + b \ln x

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Provide an appropriate response. -Explain why negative numbers do not have logarithms.

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Consider blured image, or blured image, where blured image is a po...

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Convert to an exponential equation. - log⁡864=t\log _ { 8 } 64 = \mathrm { t }


A) 64t=864 ^ { t } = 8
B) 8t=648 ^ { t } = 64
C) 864=t864 = t
D) t8=64t ^ { 8 } = 64

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Find the domain and range of the inverse of the given function. - f(x) =x−4.93f ( x ) = \sqrt [ 3 ] { x - 4.9 }


A) Domain: [4.9,∞) [ 4.9 , \infty ) ; range: [0,∞) [ 0 , \infty )
B) Domain: all real numbers; range: [4.9,∞) [ 4.9 , \infty )
C) Domain and range: all real numbers
D) Domain: all real numbers; range: [0,∞) [ 0 , \infty )

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Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic exponential function. - f(x) =3(x−1) −1f(x) =3(x-1) -1


A) Shift y=3xy = 3 ^ { x } left 1 unit(s) and up 1 unit(s)
Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic exponential function. - f(x) =3(x-1) -1 A) Shift y = 3 ^ { x } left 1 unit(s) and up 1 unit(s) B) Shift y = 3 ^ { x } left 1 unit(s) and down 1 unit(s) C) Shift y = 3 ^ { x } right 1 unit(s) and up 1 unit(s) D) Shift y = 3 ^ { x } right 1 unit(s) and dawn 1 unit(s)
B) Shift y=3xy = 3 ^ { x } left 1 unit(s) and down 1 unit(s)
Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic exponential function. - f(x) =3(x-1) -1 A) Shift y = 3 ^ { x } left 1 unit(s) and up 1 unit(s) B) Shift y = 3 ^ { x } left 1 unit(s) and down 1 unit(s) C) Shift y = 3 ^ { x } right 1 unit(s) and up 1 unit(s) D) Shift y = 3 ^ { x } right 1 unit(s) and dawn 1 unit(s)
C) Shift y=3xy = 3 ^ { x } right 1 unit(s) and up 1 unit(s)
Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic exponential function. - f(x) =3(x-1) -1 A) Shift y = 3 ^ { x } left 1 unit(s) and up 1 unit(s) B) Shift y = 3 ^ { x } left 1 unit(s) and down 1 unit(s) C) Shift y = 3 ^ { x } right 1 unit(s) and up 1 unit(s) D) Shift y = 3 ^ { x } right 1 unit(s) and dawn 1 unit(s)
D) Shift y=3xy = 3 ^ { x } right 1 unit(s) and dawn 1 unit(s)
Sketch the graph of the function. Describe how the graph can be obtained from the graph of a basic exponential function. - f(x) =3(x-1) -1 A) Shift y = 3 ^ { x } left 1 unit(s) and up 1 unit(s) B) Shift y = 3 ^ { x } left 1 unit(s) and down 1 unit(s) C) Shift y = 3 ^ { x } right 1 unit(s) and up 1 unit(s) D) Shift y = 3 ^ { x } right 1 unit(s) and dawn 1 unit(s)

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Convert to a logarithmic equation. - 53=1255 ^ { 3 } = 125


A) 3=log⁡12553 = \log _ { 125 } 5
B) 125=log⁡53125 = \log _ { 5 } 3
C) 5=log⁡31255 = \log _ { 3 } 125
D) 3=log⁡51253 = \log _ { 5 } 125

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The graph of a one-to-one function f is given. Sketch the graph of the inverse function f−1\mathrm { f } ^ { - 1 } , on the same set of axes. Use a dashed line for the inverse. - The graph of a one-to-one function f is given. Sketch the graph of the inverse function \mathrm { f } ^ { - 1 } , on the same set of axes. Use a dashed line for the inverse. - A) B) C) D)


A)
The graph of a one-to-one function f is given. Sketch the graph of the inverse function \mathrm { f } ^ { - 1 } , on the same set of axes. Use a dashed line for the inverse. - A) B) C) D)
B)
The graph of a one-to-one function f is given. Sketch the graph of the inverse function \mathrm { f } ^ { - 1 } , on the same set of axes. Use a dashed line for the inverse. - A) B) C) D)
C)
The graph of a one-to-one function f is given. Sketch the graph of the inverse function \mathrm { f } ^ { - 1 } , on the same set of axes. Use a dashed line for the inverse. - A) B) C) D)
D)
The graph of a one-to-one function f is given. Sketch the graph of the inverse function \mathrm { f } ^ { - 1 } , on the same set of axes. Use a dashed line for the inverse. - A) B) C) D)

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Using the horizontal-line test, determine whether the function is one-to-one. - f(x) =7x2−2f(x) =\frac{7}{x^{2}-2} Using the horizontal-line test, determine whether the function is one-to-one. - f(x) =\frac{7}{x^{2}-2} A) Yes B) \mathrm { No }


A) Yes
B) No\mathrm { No }

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Provide an appropriate response. -Suppose that $1000 is invested for 5 years at 4% interest, compounded annually. In what year will the most interest be earned? Why?

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The most interest will be earn...

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Find the domain and the vertical asymptote of the function. - g(x) =ln⁡(x−8) g ( x ) = \ln ( x - 8 )


A) Domain: (8,∞) ( 8 , \infty ) ; vertical asymptote: x=8x = 8
B) Domain: (−∞,∞) ( - \infty , \infty ) ; vertical asymptote: none
C) Domain: (−8,∞) ( - 8 , \infty ) ; vertical asymptote: x=−8x = - 8
D) Domain: (0,∞) ( 0 , \infty ) ; vertical asymptote: x=0x = 0

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Solve the problem. -An initial investment of $1000 is appreciated for 4 years in an account that earns 4% interest, compounded annually. Find the amount of money in the account at the end of the period.


A) $1216.65
B) $169.86
C) $1169.86
D) $1124.86

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Graph the piecewise function. - f(x) ={e−x−8, for x<−2x−2, for −2≤x<1x3, for x≥1f ( x ) = \left\{ \begin{array} { l l } e ^ { - x } - 8 , & \text { for } x < - 2 \\x - 2 , & \text { for } - 2 \leq x < 1 \\x ^ { 3 } , & \text { for } x \geq 1\end{array} \right. Graph the piecewise function. - f ( x ) = \left\{ \begin{array} { l l } e ^ { - x } - 8 , & \text { for } x < - 2 \\ x - 2 , & \text { for } - 2 \leq x < 1 \\ x ^ { 3 } , & \text { for } x \geq 1 \end{array} \right. A) B) C) D)


A)
Graph the piecewise function. - f ( x ) = \left\{ \begin{array} { l l } e ^ { - x } - 8 , & \text { for } x < - 2 \\ x - 2 , & \text { for } - 2 \leq x < 1 \\ x ^ { 3 } , & \text { for } x \geq 1 \end{array} \right. A) B) C) D)
B)
Graph the piecewise function. - f ( x ) = \left\{ \begin{array} { l l } e ^ { - x } - 8 , & \text { for } x < - 2 \\ x - 2 , & \text { for } - 2 \leq x < 1 \\ x ^ { 3 } , & \text { for } x \geq 1 \end{array} \right. A) B) C) D)
C)
Graph the piecewise function. - f ( x ) = \left\{ \begin{array} { l l } e ^ { - x } - 8 , & \text { for } x < - 2 \\ x - 2 , & \text { for } - 2 \leq x < 1 \\ x ^ { 3 } , & \text { for } x \geq 1 \end{array} \right. A) B) C) D)
D)
Graph the piecewise function. - f ( x ) = \left\{ \begin{array} { l l } e ^ { - x } - 8 , & \text { for } x < - 2 \\ x - 2 , & \text { for } - 2 \leq x < 1 \\ x ^ { 3 } , & \text { for } x \geq 1 \end{array} \right. A) B) C) D)

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Evaluate to four decimal places using a calculator. - e1.233\mathrm { e } ^ { 1.233 }


A) 7.38917.3891
B) 3.43153.4315
C) 3.35163.3516
D) 1.52031.5203

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Provide an appropriate response. -Prove that the function f is one-to-one. f(x)=x3+5f ( x ) = \sqrt [ 3 ] { x } + 5

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Assume that blured image for any numbers blured image and blured image in th...

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