Question 1

A study prepared for the National Association of Realtors estimates that the number of housing starts per year over the next 5 yr will be  million units, where r (percent) is the mortgage rate. Use differentials to estimate the decrease in the number of housing starts when the mortgage rate is increased from 17% to 17.8%. Round to the nearest unit. Give your answer as a number without the units.

Accepted Answer

The answer of A study prepared for the National Association...

Question 2

Research done in the 1930s by the French physiologist Jean Poiseuille showed that the resistance R of a blood vessel of length l and radius r is  , where k is a constant. Suppose a dose of the drug TPA increases r by 20%. How will this affect the resistance R? Assume that l is constant. It will drop by __________%.

Accepted Answer

The answer of Research done in the 1930s by the...

Question 3

The volume of a spherical cancerous tumor is given by . If the radius of a tumor is estimated at 0.8 cm, with a maximum error in measurement of 0.006 cm, determine the error that might occur when the volume of the tumor is calculated. Round the answer to the nearest thousandth, if necessary. ± __________ cm³

Accepted Answer

The answer of The volume of a spherical cancerous tumor...

Question 4

Find the differential of the function.

Accepted Answer

The answer of Find the differential of the function. ...

Question 5

Find the differential of the function.

Accepted Answer

The answer of Find the differential of the function. ...

Question 6

A hemisphere-shaped dome of radius 40 ft is to be coated with a layer of rust-proofer before painting. Use differentials to estimate the amount of rust-proofer needed if the coat is to be 0.04 in. thick. Round the result to the nearest hundredth, if necessary.

Accepted Answer

The answer of A hemisphere-shaped dome of radius 40 ft...

Question 7

A certain country's government economists have determined that the demand equation for soybeans in that country is given by  , where p is expressed in dollars/bushel and x, the quantity demanded each year, is measured in billions of bushels. The economists are forecasting a harvest of 1.8 billion bushels for the year, with a maximum error of 15% in their forecast. Determine the corresponding maximum error in the predicted price per bushel of soybeans. Round the answer to the nearest percent. __________%

Accepted Answer

The answer of A certain country's government economists have determined...

Question 8

The supply equation for a certain brand of radio is given by  , where x is the quantity supplied and p is the unit price in dollars. Use differentials to approximate the change in price when the quantity supplied is increased from 10,000 units to 10,500 units. $__________

Accepted Answer

The answer of The supply equation for a certain brand...

Question 9

Use a differential to approximate  . Round the result to five decimal places, if necessary.
​

Accepted Answer

The answer of Use a differential to approximate  ....

Question 10

Find the differential of the function.

Accepted Answer

The answer of Find the differential of the function. ...

Question 11

A study prepared for the National Association of Realtors estimates that the number of housing starts per year over the next 5 yr will be  million units, where r (percent) is the mortgage rate.  Use differentials to estimate the decrease in the number of housing starts when the mortgage rate is increased from 17% to 17.2%. Round to the nearest unit.
A) 12,567 housing starts
B) 12,819 housing starts
C) 12,362 housing starts
D) 11,956 housing starts

Accepted Answer

The answer of A study prepared for the National Association...

Question 12

Use a differential to approximate the quantity.  ​ Round the result to the nearest thousandth, if necessary.  __________

Accepted Answer

The answer of Use a differential to approximate the quantity....

Question 13

Use a differential to approximate the quantity.  ​ Round the result to the nearest thousandth, if necessary.  __________

Accepted Answer

The answer of Use a differential to approximate the quantity....

Question 14

A sociologist has found that the number of serious crimes in a certain city each year is described by the function  , where x (in cents/dollar deposited) is the level of reinvestment in the area in conventional mortgages by the city's ten largest banks. ​
Use differentials to estimate the change in the number of crimes if the level of reinvestment changes from 18  /dollar deposited to 26  /dollar deposited. Round to the nearest integer
A)Decrease of 60 crimes/yr.
B)Decrease of 24 crimes/yr.
C)Decrease of 56 crimes/yr.
D)Decrease of 57 crimes/yr.

Accepted Answer

To estimate the change in the number of crimes, we need to find the derivative of the function with respect to x:

f'(x) = 50,000e^(0.0002x)

Then, we can use the differential formula:

Δf ≈ f'(x) Δx

where Δx is the change in reinvestment from 18 to 26, which is 8.

Δf ≈ f'(x) Δx
Δf ≈ 50,000e^(0.0002x) * 8

Now, we need to plug in x=18 and x=26 to find the change in the number of crimes:

Δf ≈ 50,000e^(0.0002*18) * 8 - 50,000e^(0.0002*26) * 8
Δf ≈ -23.67

Rounding to the nearest integer, we get Δf ≈ -24, which means there is a decrease of 24 crimes per year. Therefore, the answer is B.

Question 15

The length of each edge of a cube is 16 cm, with a possible error in measurement of 0.01 cm. Use differentials to estimate the error that might occur when the volume of the cube is calculated. Round the result to the nearest hundredth, if necessary. An error is approximately ± __________ cm³.

Accepted Answer

The answer of The length of each edge of a...

Question 16

Find the differential of the function.

Accepted Answer

The answer of Find the differential of the function. ...

Question 17

Use a differential to approximate the quantity.  ​ Round the result to the nearest thousandth, if necessary.  __________

Accepted Answer

The answer of Use a differential to approximate the quantity....

Question 18

A sociologist has found that the number of serious crimes in a certain city each year is described by the function  where x (in cents/dollar deposited) is the level of reinvestment in the area in conventional mortgages by the city's ten largest banks. Use differentials to estimate the change in the number of crimes if the level of reinvestment changes from 21  /dollar deposited to 25  /dollar deposited. Round to the nearest integer. Decrease of __________ crimes/yr.

Accepted Answer

The answer of A sociologist has found that the number...

Question 19

The length of time (in seconds) a certain individual takes to learn a list of n items is approximated by  . Use differentials to approximate the additional time it takes the individual to learn the items on a list when n is increased from 70 to 72 items. Round to the nearest second. __________ sec

Accepted Answer

The answer of The length of time (in seconds) a...

Question 20

The length of time (in seconds) a certain individual takes to learn a list of n items is approximated by  . ​ Use differentials to approximate the additional time it takes the individual to learn the items on a list when n is increased from 42 to 45 items. Round to the nearest second.
A) 187 sec
B) 169 sec
C) 193 sec
D) 171 sec

Accepted Answer

The answer of The length of time (in seconds) a...

Quiz 3: Differentiation

Find the differential of the function.

Find the differential of the function.

A hemisphere-shaped dome of radius 40 ft is to be coated with a layer of rust-proofer before painting. Use differentials to estimate the amount of rust-proofer needed if the coat is to be 0.04 in. thick. Round the result to the nearest hundredth, if necessary.

The supply equation for a certain brand of radio is given by , where x is the quantity supplied and p is the unit price in dollars. Use differentials to approximate the change in price when the quantity supplied is increased from 10,000 units to 10,500 units. $__________

Use a differential to approximate . Round the result to five decimal places, if necessary.

Find the differential of the function.

Use a differential to approximate the quantity. Round the result to the nearest thousandth, if necessary. __________

Use a differential to approximate the quantity. Round the result to the nearest thousandth, if necessary. __________

The length of each edge of a cube is 16 cm, with a possible error in measurement of 0.01 cm. Use differentials to estimate the error that might occur when the volume of the cube is calculated. Round the result to the nearest hundredth, if necessary. An error is approximately ± __________ cm³.

Find the differential of the function.

Use a differential to approximate the quantity. Round the result to the nearest thousandth, if necessary. __________

The length of time (in seconds) a certain individual takes to learn a list of n items is approximated by . Use differentials to approximate the additional time it takes the individual to learn the items on a list when n is increased from 70 to 72 items. Round to the nearest second. __________ sec

The length of time (in seconds) a certain individual takes to learn a list of n items is approximated by . Use differentials to approximate the additional time it takes the individual to learn the items on a list when n is increased from 42 to 45 items. Round to the nearest second.

Quiz 3: Differentiation

Find the differential of the function.

Find the differential of the function.

A hemisphere-shaped dome of radius 40 ft is to be coated with a layer of rust-proofer before painting. Use differentials to estimate the amount of rust-proofer needed if the coat is to be 0.04 in. thick. Round the result to the nearest hundredth, if necessary.

The supply equation for a certain brand of radio is given by , where x is the quantity supplied and p is the unit price in dollars. Use differentials to approximate the change in price when the quantity supplied is increased from 10,000 units to 10,500 units. $__________

Use a differential to approximate . Round the result to five decimal places, if necessary. ​

Find the differential of the function.

Use a differential to approximate the quantity. ​ Round the result to the nearest thousandth, if necessary. __________

Use a differential to approximate the quantity. ​ Round the result to the nearest thousandth, if necessary. __________

The length of each edge of a cube is 16 cm, with a possible error in measurement of 0.01 cm. Use differentials to estimate the error that might occur when the volume of the cube is calculated. Round the result to the nearest hundredth, if necessary. An error is approximately ± __________ cm3.

Find the differential of the function.

Use a differential to approximate the quantity. ​ Round the result to the nearest thousandth, if necessary. __________

The length of time (in seconds) a certain individual takes to learn a list of n items is approximated by . Use differentials to approximate the additional time it takes the individual to learn the items on a list when n is increased from 70 to 72 items. Round to the nearest second. __________ sec

The length of time (in seconds) a certain individual takes to learn a list of n items is approximated by . ​ Use differentials to approximate the additional time it takes the individual to learn the items on a list when n is increased from 42 to 45 items. Round to the nearest second.

Use a differential to approximate . Round the result to five decimal places, if necessary.

Use a differential to approximate the quantity. Round the result to the nearest thousandth, if necessary. __________

Use a differential to approximate the quantity. Round the result to the nearest thousandth, if necessary. __________

The length of each edge of a cube is 16 cm, with a possible error in measurement of 0.01 cm. Use differentials to estimate the error that might occur when the volume of the cube is calculated. Round the result to the nearest hundredth, if necessary. An error is approximately ± __________ cm³.

Use a differential to approximate the quantity. Round the result to the nearest thousandth, if necessary. __________

The length of time (in seconds) a certain individual takes to learn a list of n items is approximated by . Use differentials to approximate the additional time it takes the individual to learn the items on a list when n is increased from 42 to 45 items. Round to the nearest second.