Southern New Hampshire University - 3-3 Module Three Problem Set PDF

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3/19/2021

Southern New Hampshire University - 3-3 Module Three Problem Set

[PRINT] MAT-140-X4714 21EW4 Precalculus, 3-3 Module Three Problem Set FLOR RIVERA, 3/17/21 at 11:40:37 PM EDT

Question1: Score 3/3

Expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of logs.

Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, .

Your response

Correct response

-2*k*ln(7)

-2*k*ln(7)

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We can expand by applying the Quotient Rule.

Apply the Quotient Rule. Simplify by writing

as

.

Simplify. Apply the Power Rule.

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Southern New Hampshire University - 3-3 Module Three Problem Set

Question2: Score 3/6

Use the properties of logarithms to expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of logs.

Your response

Correct response 5/2*log(x)-2*log(y)

Auto graded Grade: 3/3.0

Show your work and explain, in your own words, how you arrived at your answer. log10 ( √x^1/y^4) log10( √x^5/y^4 log10((x^5/y^4)1/2) 1/2* log10(x^5/y^4) 1/2*(log 10(x^5)-log log10(y^4)) 1/2*5log(x)-1/2*4loglog10(y) 5/2*l log10(x)-2 log10(y)

Ungraded Grade: 0/3.0



Total grade: 1.0×3/6 + 0.0×3/6 = 50% + 0% Feedback:

First we rewrite the argument as a power to get

.

Using the properties of exponents we have

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Southern New Hampshire University - 3-3 Module Three Problem Set

.

Since the argument is factored completely, we can write the equivalent equation by summing the logarithms of each factor.

Applying the power rule we have

.

Question3: Score 4/4

Condense the expression to a single logarithm using the properties of logarithms.

Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, .

Your response

Correct response log(x*z^3/sqrt(y))

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Southern New Hampshire University - 3-3 Module Three Problem Set

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We apply the power rule first:

.

Next we apply the quotient rule to the difference:

.

Finally, we apply the product rule to the sum:

.

Question4: Score 4/4

Use properties of logarithms to evaluate without using a calculator.

Your response 4

Correct response 4

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Southern New Hampshire University - 3-3 Module Three Problem Set

Feedback:

Use the power rule.

Rewrite the first argument with base .

Simplify.

Question5: Score 3/3

Use like bases to solve the exponential equation.

Enter the exact answer.

Your response

Correct response

-1/2

-1/2

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Southern New Hampshire University - 3-3 Module Three Problem Set

Write

and

as powers of .

To take a power of a power, multiply exponents. To multiply terms with the same base, add exponents.

By the one-to-one property the exponents must be equal. Subtract Divide by

from both sides. .

Question6: Score 4/4

Use logarithms to solve.

Enter the exact answer (i.e. keep your answer in exponential or logarithmic form, you do not need to calculate its numeric value). Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, .

Hints: Remember by the rule of exponents, that

so that you can try to factor this as where the "something" and "something else"

can be positive or negative numbers. Alternately, you could let solve first for and then for .

and this equation would be

and you can

Your response

Correct response

ln(10)

ln(10)

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Factor by the FOIL method. or

If a product is zero, then one factor must be zero.

or

Isolate the exponentials. Reject the equation in which the power equals a negative number. Solve the equation in which the power equals a positive number.

Question7: Score 4/4

Solve for the indicated value, and graph the situation showing the solution point. The formula for measuring sound intensity in decibels

is defined by the equation

using the

common (base 10) logarithm where is the intensity of the sound in watts per square meter and is the lowest level of sound that the average person can hear. How many decibels are emitted from a jet plane with a sound intensity of

watts per square meter?

Round your answer to three decimal places.

The jet plane emits Your response

Correct response

149.138

149.138±0.001

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Southern New Hampshire University - 3-3 Module Three Problem Set

decibels at

watts per square meter.

Select the correct graph of the situation showing the solution point.

Your response

Correct response

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To find the decibels emitted from the jet plane we substitute the given equation.

and

into

Substitute the given values into the equation. Simplify using exponent laws. Solve for

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.

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Southern New Hampshire University - 3-3 Module Three Problem Set

Therefore the jet plane emits decibels at showing the solution point is shown in the figure below.

watts per square meter. The situation

Question8: Score 4/4

Use the one-to-one property of logarithms to solve.

Enter the exact answers.

The field below accepts a list of numbers or formulas separated by semicolons (e.g. ).

Your response

Correct response

-5/3;5/3

-5/3; 5/3

or

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

Total grade: 1.0×1/1 = 100% Feedback:

Apply the product rule of logarithms. Apply the one-to-one property of a logarithm. Add

.

Divide by . Solve for .

Question9: Score 3/6

Atmospheric pressure

in pounds per square inch is represented by the formula

, where is the number of miles above sea level. To the nearest foot, how high is the peak of a mountain with an atmospheric pressure of pounds per square inch? (Hint: there are feet in a mile)

The mountain is Your response

Correct response

14873.76

14,873±1

Auto graded Grade: 3/3.0

feet high.

Show your work and explain, in your own words, how you arrived at your answer.

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P=14.7e−0.21x If P = 8.136 psi then 8.136=14.7e−0.21x Solve the equation for x using log properties 14.78.136=e−0.21x Apply ln to both sides ln(14.78.136)=ln(e−0.21x) Simplify ln(14.78.136)=−0.21x x=−0.21ln(14.78.136) x=−0.21ln(14.78.136)≈2.82miles Convert miles to ft 1 mile = 5280 feet 2.82mi⋅(1mi5280ft)=14873.76ft≈14890ft Ungraded Grade: 0/3.0

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Substitute

into the equation.

Divide both sides by

.

Take the natural log of both sides.

Divide by the coefficient of .

Convert to feet by multiplying by

.

Use a calculator to evaluate.

The peak of a mountain with an atmospheric pressure of feet high.

pounds per square inch is

Question10: Score 0/4

A tumor is injected with grams of Iodine-125, which has a decay rate of per day. Write an exponential model representing the amount of Iodine-125 remaining in the tumor after days. Then use the formula to find the amount of Iodine-125 that would remain in the tumor after days.

Enter the exact answer.

Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, or .

Your response

Correct response 0.5*e^(ln(0.9885)*t)

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Round to the nearest tenth of a gram.

There will be Your response

Correct response

0.5

0.2±0.1

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grams of Iodine-125 after

days.

 Total grade: 0.0×1/2 + 0.0×1/2 = 0% + 0% Feedback:

We first need to find the decay rate in order to find the formula. We are told that after one day the drug decays by , so

The continuous growth formula. Substitute

into the formula.

Divide both sides by

.

Take the natural log of both sides.

Substitute

To find the amount of Iodine-125 left in the tumor after found above.

Substitute

into the continuous growth formula.

days substitute

into the formula

.

Simplify.

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There is

Southern New Hampshire University - 3-3 Module Three Problem Set

grams of Iodine-125 left in the tumor after

days.

Question11: Score 4/4

A formula for calculating the magnitude of an earthquake is

that uses the

common (base 10) logarithm. This is called the Moment Magnitude Scale (MMS), an alternative to the more well known Richter Scale. One earthquake has magnitude on the MMS. If a second earthquake has times as much energy as the first, find the magnitude of the second quake.

Round to the nearest hundredth.

The magnitude of the second earthquake was Your response

Correct response

5.75

5.75±0.01

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.

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If the second earthquake has times as much energy as the first, we must find the amount of energy of the first earthquake. Substitute into the equation to solve for the amount of energy.

Substitute Divide by

. .

Rewrite as an exponential. Multiply by

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Southern New Hampshire University - 3-3 Module Three Problem Set

The second earthquake has formula and solve for .

times as much energy. So substitute

into the

Substitute

into formula.

Simplify. Evaluate using a calculator or spreadsheet.

The magnitude of the second earthquake was

.

Question12: Score 4/4

The equation

models the number of people in a town who have heard a

rumor after days. As increases without bound, what value does answer.

approach? Interpret your

How many people started the rumor? Your response 9

Correct response 9

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approaches Your response

Correct response

450

450

Your response

Correct response

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.

is limited by the carrying capacity of the town. Feedback:

is limited by the carrying capacity of the town.

Correct.

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This is a logistical growth model. The carrying capacity, or limiting value is the value that the function approaches as increases without bound. In this case, approaches the carrying capacity of the town, .

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