<< Chapter < Page Chapter >> Page >
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

(1+cosA)(1-cosA)=sin^2A
BINCY Reply
good
Neha
why I'm sending you solved question
Mirza
Teach me abt the echelon method
Khamis
exact value of cos(π/3-π/4)
Ankit Reply
What is differentiation?
Intakhab Reply
modul questions trigonometry
Thamarai Reply
(1+cosA)(1-cosA)=sin^2A
BINCY
differentiate f(t)=1/4t to the power 4 +8
Jessica Reply
I need trigonometry,polynomial
duru Reply
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Augustine
Why is 7 on top
Bertha Reply
simplify cot x / csc x
Catherine Reply
👉🌹Solve🌻 Given that: cotx/cosx =cosx/sinx/cosx =1/sinx =cosecx Ans.
Vijay
what is the period of cos?
SIYAMTHEMBA Reply
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Patrick
simplify: cot x/csc x
Catherine
sorry i didnt realize you were actually asking someone else to put their question on here. i thought this was where i was supposed to.
Catherine
some to dereve formula for bulky density
kurash
Solve Given that: cotx/cosx =cosx/sinx/cosx =1/sinx =cosecx Ans.
Vijay
if tan alpha + beta is equal to sin x + Y then prove that X square + Y square - 2 I got hyperbole 2 Beta + 1 is equal to zero
Rahul Reply
questions
Thamarai
ok
AjA
sin^4+sin^2=1, prove that tan^2-tan^4+1=0
SAYANTANI Reply
what is the formula used for this question? "Jamal wants to save $54,000 for a down payment on a home. How much will he need to invest in an account with 8.2% APR, compounding daily, in order to reach his goal in 5 years?"
Kuz Reply
i don't need help solving it I just need a memory jogger please.
Kuz
A = P(1 + r/n) ^rt
Dale
how to solve an expression when equal to zero
Mintah Reply
its a very simple
Kavita
gave your expression then i solve
Kavita
Hy guys, I have a problem when it comes on solving equations and expressions, can you help me 😭😭
Thuli
Tomorrow its an revision on factorising and Simplifying...
Thuli
ok sent the quiz
kurash
send
Kavita
Hi
Masum
What is the value of log-1
Masum
the value of log1=0
Kavita
Log(-1)
Masum
What is the value of i^i
Masum
log -1 is 1.36
kurash
No
Masum
no I m right
Kavita
No sister.
Masum
no I m right
Kavita
tan20°×tan30°×tan45°×tan50°×tan60°×tan70°
Joju Reply
jaldi batao
Joju
Find the value of x between 0degree and 360 degree which satisfy the equation 3sinx =tanx
musah Reply

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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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