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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 )

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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

Why is b in the answer
Dahsolar Reply
how do you work it out?
Brad Reply
answer
Ernest
heheheehe
Nitin
(Pcos∅+qsin∅)/(pcos∅-psin∅)
John Reply
how to do that?
Rosemary Reply
what is it about?
Amoah
how to answer the activity
Chabelita Reply
how to solve the activity
Chabelita
solve for X,,4^X-6(2^)-16=0
Alieu Reply
x4xminus 2
Lominate
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harish Reply
t he silly nut company makes two mixtures of nuts: mixture a and mixture b. a pound of mixture a contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for $4. a pound of mixture b contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for $5. the company has 1080
ZAHRO Reply
If  , , are the roots of the equation 3 2 0, x px qx r     Find the value of 1  .
Swetha Reply
Parts of a pole were painted red, blue and yellow. 3/5 of the pole was red and 7/8 was painted blue. What part was painted yellow?
Patrick Reply
Parts of the pole was painted red, blue and yellow. 3 /5 of the pole was red and 7 /8 was painted blue. What part was painted yellow?
Patrick
how I can simplify algebraic expressions
Katleho Reply
Lairene and Mae are joking that their combined ages equal Sam’s age. If Lairene is twice Mae’s age and Sam is 69 yrs old, what are Lairene’s and Mae’s ages?
Mary Reply
23yrs
Yeboah
lairenea's age is 23yrs
ACKA
hy
Katleho
Ello everyone
Katleho
Laurene is 46 yrs and Mae is 23 is
Solomon
hey people
christopher
age does not matter
christopher
solve for X, 4^x-6(2*)-16=0
Alieu
prove`x^3-3x-2cosA=0 (-π<A<=π
Mayank Reply
create a lesson plan about this lesson
Rose Reply
Excusme but what are you wrot?

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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