<< 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
Got questions? Get instant answers now!
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.
Got questions? Get instant answers now!
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
Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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.
Got questions? Get instant answers now!

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.
Got questions? Get instant answers now!

Rewrite log 8.5 ( 614.125 ) = a as an equivalent exponential equation.

8.5 a = 614.125

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

x = ( 1 7 ) 2 = 1 49

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

ln ( 0.716 ) 0.334

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

log t ( 12 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

no solution

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

x = ln ( 9 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Graph of the table’s values.
Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Graph of the table’s values.
Got questions? Get instant answers now!
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
Got questions? Get instant answers now!
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

Graph of the table’s values.
Got questions? Get instant answers now!

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask