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x f(x)
1 409.4
2 260.7
3 170.4
4 110.6
5 74
6 44.7
7 32.4
8 19.5
9 12.7
10 8.1
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x f(x)
0.15 36.21
0.25 28.88
0.5 24.39
0.75 18.28
1 16.5
1.5 12.99
2 9.91
2.25 8.57
2.75 7.23
3 5.99
3.5 4.81

logarithmic; y = 16.68718 9.71860 ln ( x )

Graph of the table’s values.
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x f(x)
0 9
2 22.6
4 44.2
5 62.1
7 96.9
8 113.4
10 133.4
11 137.6
15 148.4
17 149.3
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Practice test

The population of a pod of bottlenose dolphins is modeled by the function A ( t ) = 8 ( 1.17 ) t , where t is given in years. To the nearest whole number, what will the pod population be after 3 years?

About 13 dolphins.

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Find an exponential equation that passes through the points (0, 4) and (2, 9) .

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Drew wants to save $2,500 to go to the next World Cup. To the nearest dollar, how much will he need to invest in an account now with 6.25 % APR, compounding daily, in order to reach his goal in 4 years?

$ 1,947

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An investment account was opened with an initial deposit of $9,600 and earns 7.4 % interest, compounded continuously. How much will the account be worth after 15 years?

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Graph the function f ( x ) = 5 ( 0.5 ) x and its reflection across the y -axis on the same axes, and give the y -intercept.

y -intercept: ( 0 ,  5 )

Graph of f(-x)=5(0.5)^-x in blue and f(x)=5(0.5)^x in orange.
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The graph shows transformations of the graph of f ( x ) = ( 1 2 ) x . What is the equation for the transformation?

Graph of f(x)= (1/2)^x.
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Rewrite log 8.5 ( 614.125 ) = a as an equivalent exponential equation.

8.5 a = 614.125

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Rewrite e 1 2 = m as an equivalent logarithmic equation.

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Solve for x by converting the logarithmic equation l o g 1 7 ( x ) = 2 to exponential form.

x = ( 1 7 ) 2 = 1 49

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Evaluate log ( 10,000,000 ) without using a calculator.

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Evaluate ln ( 0.716 ) using a calculator. Round to the nearest thousandth.

ln ( 0.716 ) 0.334

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Graph the function g ( x ) = log ( 12 6 x ) + 3.

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State the domain, vertical asymptote, and end behavior of the function f ( x ) = log 5 ( 39 13 x ) + 7.

Domain: x < 3 ; Vertical asymptote: x = 3 ; End behavior: x 3 , f ( x ) and x , f ( x )

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Rewrite log ( 17 a 2 b ) as a sum.

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Rewrite log t ( 96 ) log t ( 8 ) in compact form.

log t ( 12 )

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Rewrite log 8 ( a 1 b ) as a product.

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Use properties of logarithm to expand ln ( y 3 z 2 x 4 3 ) .

3 ln ( y ) + 2 ln ( z ) + ln ( x 4 ) 3

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Condense the expression 4 ln ( c ) + ln ( d ) + ln ( a ) 3 + ln ( b + 3 ) 3 to a single logarithm.

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Rewrite 16 3 x 5 = 1000 as a logarithm. Then apply the change of base formula to solve for x using the natural log. Round to the nearest thousandth.

x = ln ( 1000 ) ln ( 16 ) + 5 3 2.497

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Solve ( 1 81 ) x 1 243 = ( 1 9 ) 3 x 1 by rewriting each side with a common base.

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Use logarithms to find the exact solution for 9 e 10 a 8 5 = 41 . If there is no solution, write no solution .

a = ln ( 4 ) + 8 10

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Find the exact solution for 10 e 4 x + 2 + 5 = 56. If there is no solution, write no solution .

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Find the exact solution for 5 e 4 x 1 4 = 64. If there is no solution, write no solution .

no solution

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Find the exact solution for 2 x 3 = 6 2 x 1 . If there is no solution, write no solution .

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Find the exact solution for e 2 x e x 72 = 0. If there is no solution, write no solution .

x = ln ( 9 )

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Use the definition of a logarithm to find the exact solution for 4 log ( 2 n ) 7 = 11

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Use the one-to-one property of logarithms to find an exact solution for log ( 4 x 2 10 ) + log ( 3 ) = log ( 51 ) If there is no solution, write no solution .

x = ± 3 3 2

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The formula for measuring sound intensity in decibels D is defined by the equation D = 10 log ( I I 0 ) , where I is the intensity of the sound in watts per square meter and I 0 = 10 12 is the lowest level of sound that the average person can hear. How many decibels are emitted from a rock concert with a sound intensity of 4.7 10 1 watts per square meter?

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A radiation safety officer is working with 112 grams of a radioactive substance. After 17 days, the sample has decayed to 80 grams. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest day, what is the half-life of this substance?

f ( t ) = 112 e .019792 t ; half-life: about 35 days

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Write the formula found in the previous exercise as an equivalent equation with base e . Express the exponent to five significant digits.

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A bottle of soda with a temperature of 71° Fahrenheit was taken off a shelf and placed in a refrigerator with an internal temperature of 35° F . After ten minutes, the internal temperature of the soda was 63° F . Use Newton’s Law of Cooling to write a formula that models this situation. To the nearest degree, what will the temperature of the soda be after one hour?

T ( t ) = 36 e 0.025131 t + 35 ; T ( 60 ) 43 o F

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The population of a wildlife habitat is modeled by the equation P ( t ) = 360 1 + 6.2 e 0.35 t , where t is given in years. How many animals were originally transported to the habitat? How many years will it take before the habitat reaches half its capacity?

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Enter the data from [link] into a graphing calculator and graph the resulting scatter plot. Determine whether the data from the table would likely represent a function that is linear, exponential, or logarithmic.

x f(x)
1 3
2 8.55
3 11.79
4 14.09
5 15.88
6 17.33
7 18.57
8 19.64
9 20.58
10 21.42

logarithmic

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The population of a lake of fish is modeled by the logistic equation P ( t ) = 16 , 120 1 + 25 e 0.75 t , where t is time in years. To the nearest hundredth, how many years will it take the lake to reach 80 % of its carrying capacity?

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For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to five decimal places.

x f(x)
1 20
2 21.6
3 29.2
4 36.4
5 46.6
6 55.7
7 72.6
8 87.1
9 107.2
10 138.1

exponential; y = 15.10062 ( 1.24621 ) x

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x f(x)
3 13.98
4 17.84
5 20.01
6 22.7
7 24.1
8 26.15
9 27.37
10 28.38
11 29.97
12 31.07
13 31.43
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x f(x)
0 2.2
0.5 2.9
1 3.9
1.5 4.8
2 6.4
3 9.3
4 12.3
5 15
6 16.2
7 17.3
8 17.9

logistic; y = 18.41659 1 + 7.54644 e 0.68375 x

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Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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