Question 1

Write the word or phrase that best completes each statement or answers the question.
-Use the formula $\mathrm { D } = 10.0 \log \left( \mathrm { S } / \mathrm { S } _ { 0 } \right)$, where the loudness of a sound in decibels is determined by $\mathrm { S }$, the number of watt $/ \mathrm { m } ^ { 2 }$ produced by the soundwave, and $\mathrm { S } _ { 0 } = 1.00 \times 10 ^ { - 12 } \mathrm { watt } / \mathrm { m } ^ { 2 }$. What is the intensity in watt/ $/ \mathrm { m } ^ { 2 }$ of a noise measured at 37 decibels? (Round to the nearest tenth.)
A) $4.0 \times 10 ^ { 13 } \mathrm { watt } / \mathrm { m } ^ { 2 }$
B) $3.7 \times 10 ^ { - 10 } \mathrm { watt } / \mathrm { m } ^ { 2 }$
C) $5.0 \times 10 ^ { - 8 } \mathrm { watt } / \mathrm { m } ^ { 2 }$
D) $5.0 \times 10 ^ { - 9 } \mathrm { watt } / \mathrm { m } ^ { 2 }$

Accepted Answer

The answer of Write the word or phrase that best...

Question 2

Write the word or phrase that best completes each statement or answers the question.
-Suppose the government wants to impose a tax on fossil fuels to reduce carbon emissions. The cost benefit is modeled by $\ln ( 1 - P ) = - 0.0034 - 0.0047 x$, where $x$ represents the dollars of tax per ton of carbon emitted and $\mathrm { P }$ represents the percent reduction in emissions of carbon. ( $\mathrm { P }$ is in decimal form.) Determine $\mathrm { P }$ when $\mathrm { x } = 54$. Round to three decimal places.
A) $0.227$
B) $1.773$
C) $- 0.222$
D) $- 0.17$

Accepted Answer

To find $P$ when $x = 54$, substitute $x$ into the equation: $\ln(1 - P) = -0.0034 - 0.0047(54)$. Solve for $P$ to get $P = 0.227$.

Question 3

Write the word or phrase that best completes each statement or answers the question.
-The height in meters of women of a certain tribe is approximated by $h = 0.52 + 2 \log ( \mathrm { t } / 3 )$ where $t$ is the woman's age in years and $1 \leq \mathrm { t } \leq 20$. Estimate the height (to the nearest hundredth) of a woman of the tribe 4 years of age. (Round to the nearest hundredth.)
A) $0.52 \mathrm {~m}$
B) $1.12 \mathrm {~m}$
C) $0.77 \mathrm {~m}$
D) $0.96 \mathrm {~m}$

Accepted Answer

The answer of Write the word or phrase that best...

Question 4

Write the word or phrase that best completes each statement or answers the question.
-A lake is stocked with 559 fish of a new variety. The size of the lake, the availability of food, and the number of other fish restrict growth in the lake to a limiting value of 3493 . The population of fish in the lake after time $t$, in months, is given by the function $P ( t ) = \frac { 3493 } { 1 + 4.27 e ^ { - 0.36 t } }$. Find the population after 20 months.
A) 3497 fish
B) 3492 fish
C) 3482 fish
D) 3472 fish

Accepted Answer

To find the population after 20 months, substitute $t = 20$ into the given function and calculate $P(20)$. $P(20) = \frac{3493}{1 + 4.27e^{-0.36(20)}}$. Calculating this gives a value close to 3482, making option C correct.

Question 5

Write the word or phrase that best completes each statement or answers the question.
-Many states have passed laws against smoking in public places since January. The total number of states, $N$, that have passed a no smoking law, $t$ months after January is given by the function $ \mathrm{N}(\mathrm{t})=\frac{50}{1+18 \mathrm{e}^{-0.7 \mathrm{t}}} $. How many states had passed a law in January? Round to the nearest thousandth.

A) $0.263$
B) $2.632$
C) $1.316$
D) 0

Accepted Answer

The answer of Write the word or phrase that best...

Question 6

Write the word or phrase that best completes each statement or answers the question.
-The hydrogen potential, $\mathrm { pH }$, of a substance is defined by $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]$, where $\left[ \mathrm { H } ^ { + } \right]$is measured in moles per liter. Find the pH of a sample of lake water whose $\left[ \mathrm { H } ^ { + } \right]$is $3.05 \times 10 ^ { - 9 }$ moles per liter. (Round to the nearest tenth.)
A) $6.4$
B) $10.1$
C) $8.5$
D) $7.3$

Accepted Answer

The pH is calculated as $-\log(3.05 \times 10^{-9})$, which equals approximately 8.5 when rounded to the nearest tenth.

Question 7

Write the word or phrase that best completes each statement or answers the question.
-Use the formula $\mathrm { D } = 10.0 \log \left( \mathrm { S } / \mathrm { S } _ { 0 } \right)$, where the loudness of a sound in decibels is determined by $\mathrm { S }$, the number of watt $/ \mathrm { m } ^ { 2 }$ produced by the soundwave, and $\mathrm { S } _ { 0 } = 1.00 \times 10 ^ { - 12 } \mathrm { watt } / \mathrm { m } ^ { 2 }$. A certain noise produces $2.54 \times 10 ^ { - 4 } \mathrm { watt } / \mathrm { m } ^ { 2 }$ of power. What is the decibel level of this noise? (Round to the nearest unit.)
A) 8 decibels
B) 74 decibels
C) 194 decibels
D) 84 decibels

Accepted Answer

Using the formula, $D = 10.0 \log \left( \frac{2.54 \times 10^{-4}}{1.00 \times 10^{-12}} \right)$, calculate the decibel level: $D = 10.0 \log (2.54 \times 10^8) \approx 84$ decibels.

Question 8

Write the word or phrase that best completes each statement or answers the question.
-Suppose that $y = \frac { 2 - \log ( 100 - x ) } { 0.29 }$ can be used to calculate the number of years $y$ for x percent of a population of 222 web-footed sparrows to die. Approximate the percentage (to the nearest whole per cent) of web-footed sparrows that died after 5 years.
A) $92 \%$
B) $96 \%$
C) $94 \%$
D) $98 \%$

Accepted Answer

To find the percentage of web-footed sparrows that died after 5 years, we substitute $y = 5$ into the given equation and solve for $x$. The equation becomes $5 = \frac{2 - \log(100 - x)}{0.29}$. Solving for $x$ gives approximately $96\%$.

Question 9

Write the word or phrase that best completes each statement or answers the question.
-Suppose $f ( x ) = 32.1 + 1.2 \log ( x + 1 )$ models salinity of ocean water to depths of 1000 meters at a certain latitude. $x$ is the depth in meters and $f ( x )$ is in grams of salt per kilogram of seawater. Approximate the depth (to the nearest tenth of a meter) where the salinity equals 34 .
A) $37.3 \mathrm {~g} / \mathrm { kg }$
B) $39.3 \mathrm {~g} / \mathrm { kg }$
C) $- 1.0 \mathrm {~g} / \mathrm { kg }$
D) $- 0.9 \mathrm {~g} / \mathrm { kg }$

Accepted Answer

The correct answer is A because 34 is closest to 32.1 + 1.2 log (37.3 + 1).

Question 10

Write the word or phrase that best completes each statement or answers the question.
-Suppose $f ( x ) = 33.1 + 1.4 \log ( x + 1 )$ models salinity of ocean water to depths of 1000 meters at a certain latitude. $x$ is the depth in meters and $f ( x )$ is in grams of salt per kilogram of seawater. Approximate the salinity (to the nearest hundredth) when the depth is 262 meters.
A) $78.70 \mathrm {~g} / \mathrm { kg }$
B) $36.49 \mathrm {~g} / \mathrm { kg }$
C) $- 29.71 \mathrm {~g} / \mathrm { kg }$
D) $81.50 \mathrm {~g} / \mathrm { kg }$

Accepted Answer

To find the salinity at 262 meters, substitute $x = 262$ into the given model: $f(262) = 33.1 + 1.4\log(262 + 1)$. Calculate the value inside the logarithm first, which is $263$, then calculate the logarithm and multiply by $1.4$, and finally add $33.1$. This results in approximately $36.49 \mathrm {~g} / \mathrm { kg }$.

Question 11

Write the word or phrase that best completes each statement or answers the question.
-A lake is stocked with 452 fish of a new variety. The size of the lake, the availability of food, and the number of other fish restrict growth in the lake to a limiting value of 2825 . The population of fish in the lake after time $t$, in months, is given by the function $P ( t ) = \frac { 2825 } { 1 + 5.77 e ^ { - 0.28 t } }$. After how many months will the population be 2600 ?
A) $15 \mathrm { mo }$
B) $7 \mathrm { mo }$
C) $17 \mathrm { mo }$
D) $12 \mathrm { mo }$

Accepted Answer

To find the time $t$ when the population will be 2600, we substitute $P(t) = 2600$ into the given function and solve for $t$:$$2600 = \frac{2825}{1 + 5.77e^{-0.28t}}$$Solving this equation for $t$ gives $t \approx 15$ months.

Quiz 4: Inverse, Exponential, and Logarithmic Functions