Question 1

Graph the function $g ( x ) = 2 ^ { x + 1 }$ , not by plotting points but by applying your knowledge of the general shape of graphs of the form $a ^ { x }$ . State the domain, range, and asymptote of the function.

Accepted Answer

$\text { Domain } ( - \infty , \infty ) \text {, Range } ( 0 , \infty ) \text {, Asymptote } y = 0$

Question 2

If $4500 is invested at an interest rate of 6.25% per year, compounded continuously, find the value of the investment after the given number of years.
(a) 3 years
(b) 6 years
(c) 9 years

Accepted Answer

a) $5428.04 (b) $6547.46 (c) $7897.75

Question 3

Graph the function, not by plotting points, but by starting from the graph of $y = e ^ { x }$ . State the domain, range, and asymptote. $h ( x ) = e ^ { x + 1 } - 5$

Accepted Answer

Domain: $( - \infty , \infty )$ ; Range: $( - 5 , \infty )$ ; Asymptote: $y = - 5$

Question 4

A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function $m ( t ) = 13 e ^ { - 0.015 t }$ where $m ( t )$ is measured in kilograms. Round your answers to three decimal places.
a) Find the mass at time $t = 0$ .
b) How much of the mass remains after 100 days?

Accepted Answer

The answer of A radioactive substance decays in such a...

Question 5

Sketch the graph of the function $h ( x ) = ( 0.6 ) ^ { x }$ by making a table of values. Use a calculator if necessary.

Accepted Answer

The answer of Sketch the graph of the function \(h...

Question 6

If $f ( x ) = 5 ^ { x }$ , show that $\frac { f ( x + h ) - f ( x ) } { h } = 5 ^ { x } \left( \frac { 5 ^ { h } - 1 } { h } \right)$ .

Accepted Answer

The answer of If \(f ( x ) = 5...

Question 7

Graph the function, not by plotting points, but by starting from the graph of $y = e ^ { x }$ . State the domain, range, and asymptote. $h ( x ) = e ^ { x - 3 } + 5$

Accepted Answer

The answer of Graph the function, not by plotting points,...

Question 8

If $2500 is invested at an interest rate of 6.25% per year, compounded continuously, find the value of the investment after the given number of years.
(a) 3 years
(b) 6 years
(c) 9 years

Accepted Answer

The answer of If $2500 is invested at an interest...

Question 9

Graph the function $y = 2 ^ { | x | }$ , not by plotting points but by applying your knowledge of the general shape of graphs of the form $a ^ { x }$ . State the domain, range, and asymptote of the function.

Accepted Answer

The answer of Graph the function \(y = 2 ^...

Question 10

Sketch the graph of the function $f ( x ) = \left( \frac { 3 } { 2 } \right) ^ { x }$ by making a table of values. Use a calculator if necessary.

Accepted Answer

The answer of Sketch the graph of the function \(f...

Question 11

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. $g ( x ) = ( 2 / 3 ) ^ { 2 x } ; g ( 0.7 ) , g ( \sqrt { 2 } / 2 ) , g ( 1 / \pi ) , g ( 1 / 3 )$

Accepted Answer

The answer of Use a calculator to evaluate the function...

Question 12

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. $h ( x ) = e ^ { - x } , \quad h ( 1 ) , h ( \sqrt { 2 } ) , h ( - 3 ) , h ( 1 / 2 )$

Accepted Answer

The answer of Use a calculator to evaluate the function...

Question 13

Graph the function $y = - 3 + 2 \left( 1 + 3 ^ { x } \right)$ , not by plotting points but by applying your knowledge of the general shape of graphs of the form $a ^ { x }$ . State the domain, range, and asymptote of the function.

Accepted Answer

The answer of Graph the function \(y = - 3...

Question 14

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. $h ( x ) = 3 e ^ { x } , \quad h ( 3 ) , h ( 0.23 ) , h ( 1 ) , h ( - 2 )$

Accepted Answer

The answer of Use a calculator to evaluate the function...

Question 15

Find the exponential function whose graph is given.

Accepted Answer

The answer of Find the exponential function whose graph is...

Question 16

A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function $m ( t ) = 13 e ^ { - 0.015 t }$ where $m ( t )$ is measured in kilograms. Round your answers to three decimal places.
a) Find the mass at time $t = 0$ .
b) How much of the mass remains after 50 days?

Accepted Answer

The answer of A radioactive substance decays in such a...

Question 17

For the function $y = \frac { 2 ^ { 2 / x } } { x }$ , ( $x < 0$ ), use a graphing calculator to find, correct to two decimal places, 
(a) the intervals on which the function is increasing or decreasing, and
(b) the range of the function.

Accepted Answer

The answer of For the function \(y = \frac {...

Question 18

If $10,000 is invested at an interest rate of 5% per year, compounded semiannually, find the value of the investment after the given number of years.
(a) 5 years
(b) 10 years
(c) 15 years

Accepted Answer

The answer of If $10,000 is invested at an interest...

Question 19

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. $f ( x ) = 2 ^ { x } , \quad f ( 0.5 ) , f ( \sqrt { 2 } ) , f ( \pi ) , f ( 1 / 3 )$

Accepted Answer

The answer of Use a calculator to evaluate the function...

Question 20

If $10,000 is invested at an interest rate of 4% per year, compounded semiannually, find the value of the investment after the given number of years.
(a) 5 years
(b) 10 years
(c) 15 years

Accepted Answer

The answer of If $10,000 is invested at an interest...

Quiz 4: Exponential and Logarithmic Functions

Graph the function g(x)=2x+1g ( x ) = 2 ^ { x + 1 }g(x)=2x+1 , not by plotting points but by applying your knowledge of the general shape of graphs of the form axa ^ { x }ax . State the domain, range, and asymptote of the function.

If $4500 is invested at an interest rate of 6.25% per year, compounded continuously, find the value of the investment after the given number of years. (a) 3 years (b) 6 years (c) 9 years

Graph the function, not by plotting points, but by starting from the graph of y=exy = e ^ { x }y=ex . State the domain, range, and asymptote. h(x)=ex+1−5h ( x ) = e ^ { x + 1 } - 5h(x)=ex+1−5

Sketch the graph of the function h(x)=(0.6)xh ( x ) = ( 0.6 ) ^ { x }h(x)=(0.6)x by making a table of values. Use a calculator if necessary.

If f(x)=5xf ( x ) = 5 ^ { x }f(x)=5x , show that f(x+h)−f(x)h=5x(5h−1h)\frac { f ( x + h ) - f ( x ) } { h } = 5 ^ { x } \left( \frac { 5 ^ { h } - 1 } { h } \right)hf(x+h)−f(x)​=5x(h5h−1​) .

Graph the function, not by plotting points, but by starting from the graph of y=exy = e ^ { x }y=ex . State the domain, range, and asymptote. h(x)=ex−3+5h ( x ) = e ^ { x - 3 } + 5h(x)=ex−3+5

If $2500 is invested at an interest rate of 6.25% per year, compounded continuously, find the value of the investment after the given number of years. (a) 3 years (b) 6 years (c) 9 years

Graph the function y=2∣x∣y = 2 ^ { | x | }y=2∣x∣ , not by plotting points but by applying your knowledge of the general shape of graphs of the form axa ^ { x }ax . State the domain, range, and asymptote of the function.

Sketch the graph of the function f(x)=(32)xf ( x ) = \left( \frac { 3 } { 2 } \right) ^ { x }f(x)=(23​)x by making a table of values. Use a calculator if necessary.

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. g(x)=(2/3)2x;g(0.7),g(2/2),g(1/π),g(1/3)g ( x ) = ( 2 / 3 ) ^ { 2 x } ; g ( 0.7 ) , g ( \sqrt { 2 } / 2 ) , g ( 1 / \pi ) , g ( 1 / 3 )g(x)=(2/3)2x;g(0.7),g(2​/2),g(1/π),g(1/3)

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. h(x)=e−x,h(1),h(2),h(−3),h(1/2)h ( x ) = e ^ { - x } , \quad h ( 1 ) , h ( \sqrt { 2 } ) , h ( - 3 ) , h ( 1 / 2 )h(x)=e−x,h(1),h(2​),h(−3),h(1/2)

Graph the function y=−3+2(1+3x)y = - 3 + 2 \left( 1 + 3 ^ { x } \right)y=−3+2(1+3x) , not by plotting points but by applying your knowledge of the general shape of graphs of the form axa ^ { x }ax . State the domain, range, and asymptote of the function.

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. h(x)=3ex,h(3),h(0.23),h(1),h(−2)h ( x ) = 3 e ^ { x } , \quad h ( 3 ) , h ( 0.23 ) , h ( 1 ) , h ( - 2 )h(x)=3ex,h(3),h(0.23),h(1),h(−2)

Find the exponential function whose graph is given.

For the function y=22/xxy = \frac { 2 ^ { 2 / x } } { x }y=x22/x​ , ( x<0x < 0x<0 ), use a graphing calculator to find, correct to two decimal places, (a) the intervals on which the function is increasing or decreasing, and (b) the range of the function.

If $10,000 is invested at an interest rate of 5% per year, compounded semiannually, find the value of the investment after the given number of years. (a) 5 years (b) 10 years (c) 15 years

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. f(x)=2x,f(0.5),f(2),f(π),f(1/3)f ( x ) = 2 ^ { x } , \quad f ( 0.5 ) , f ( \sqrt { 2 } ) , f ( \pi ) , f ( 1 / 3 )f(x)=2x,f(0.5),f(2​),f(π),f(1/3)

If $10,000 is invested at an interest rate of 4% per year, compounded semiannually, find the value of the investment after the given number of years. (a) 5 years (b) 10 years (c) 15 years

Graph the function $g ( x ) = 2 ^ { x + 1 }$ , not by plotting points but by applying your knowledge of the general shape of graphs of the form $a ^ { x }$ . State the domain, range, and asymptote of the function.

Graph the function, not by plotting points, but by starting from the graph of $y = e ^ { x }$ . State the domain, range, and asymptote. $h ( x ) = e ^ { x + 1 } - 5$

Sketch the graph of the function $h ( x ) = ( 0.6 ) ^ { x }$ by making a table of values. Use a calculator if necessary.

If $f ( x ) = 5 ^ { x }$ , show that $\frac { f ( x + h ) - f ( x ) } { h } = 5 ^ { x } \left( \frac { 5 ^ { h } - 1 } { h } \right)$ .

Graph the function, not by plotting points, but by starting from the graph of $y = e ^ { x }$ . State the domain, range, and asymptote. $h ( x ) = e ^ { x - 3 } + 5$

Sketch the graph of the function $f ( x ) = \left( \frac { 3 } { 2 } \right) ^ { x }$ by making a table of values. Use a calculator if necessary.

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. $g ( x ) = ( 2 / 3 ) ^ { 2 x } ; g ( 0.7 ) , g ( \sqrt { 2 } / 2 ) , g ( 1 / \pi ) , g ( 1 / 3 )$

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. $h ( x ) = e ^ { - x } , \quad h ( 1 ) , h ( \sqrt { 2 } ) , h ( - 3 ) , h ( 1 / 2 )$

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. $h ( x ) = 3 e ^ { x } , \quad h ( 3 ) , h ( 0.23 ) , h ( 1 ) , h ( - 2 )$

For the function $y = \frac { 2 ^ { 2 / x } } { x }$ , ( $x < 0$ ), use a graphing calculator to find, correct to two decimal places, (a) the intervals on which the function is increasing or decreasing, and (b) the range of the function.

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. $f ( x ) = 2 ^ { x } , \quad f ( 0.5 ) , f ( \sqrt { 2 } ) , f ( \pi ) , f ( 1 / 3 )$