# Section 6 -3 Estimating Rates of Change

Business

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Q 2Q 2

To get a good estimate of the value of we should use a very short interval to calculate the average rate of change for .

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Q 11Q 11

Use an increment of 0.2 to estimate the value of at if .
A) 0
B) 4.92
C) 24.6
D) None of the above

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Q 12Q 12

Use an increment of 0.02 to estimate the value of at if .
A) 0.0404
B) 2.02
C) 0
D) None of the above

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Q 13Q 13

Use an increment of 0.3 to estimate the value of at if .Round your answer to two decimal places.
A) -0.13
B) -0.04
C) 0.00
D) None of the above

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Q 14Q 14

Use an increment of 0.03 to estimate the value of at if .Round your answer to two decimal places.
A) 0.02
B) 0.82
C) 0
D) None of the above

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Q 15Q 15

Use an increment of 0.3 to estimate the value of at if .Round your answer to two decimal places.
A) 0.44
B) 1.47
C) 0.00
D) None of the above

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Q 16Q 16

A balloon is floating upward.Its height in feet t seconds after release is given by the function .We know that and is 4 when t is 3.Use this information to estimate the height of the balloon 9 seconds after release.
A) 24 feet
B) 15 feet
C) 35 feet
D) None of the above

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Q 17Q 17

Water is draining from a pond.The amount of water, in gallons, remaining in the pond t minutes after draining begins is given by the function .We know that and is -579 when t is 9.Use this information to estimate the amount of water in the pond 16 minutes after draining begins.
A) 2,309 gallons
B) 1,160 gallons
C) 4,634 gallons
D) None of the above

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Q 18Q 18

A ball is tossed upward and then falls to the ground.Its height after t seconds is given by the function .During the period the rock is rising, what can be said about ?
A) is positive.
B) is negative.
C) is zero.
D) None of the above

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Q 19Q 19

A ball is tossed upward and then falls to the ground.Its height after t seconds is given by the function .During the period the rock is falling, what can be said about ?
A) is positive.
B) is negative.
C) is zero.
D) None of the above

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Q 20Q 20

A ball is tossed upward and then falls to the ground.Its height after t seconds is given by the function .At the time the rock reaches its peak, what can be said about ?
A) is positive.
B) is negative.
C) is zero.
D) None of the above

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Q 21Q 21

The profit earned when n items are produced is given by the function .If increasing production will result in an increase in profits, what can be said about marginal profit ?
A) is positive.
B) is negative.
C) is zero.
D) is linear.

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Q 22Q 22

The profit earned when n items are produced is given by the function .If increasing production will result in a decrease in profits, what can be said about marginal profit ?
A) is positive.
B) is negative.
C) is zero.
D) is linear.

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Q 23Q 23

The profit earned when n items are produced is given by the function .If either increasing production or decreasing production will result in a decrease in profits, what can be said about marginal profit ?
A) is positive.
B) is negative.
C) is zero.
D) is linear.

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Q 24Q 24

A population changes with time.Its level after t years is given by the function .Over a certain period, the population is growing.What can be said about over this period?
A) is positive.
B) is negative.
C) is zero.
D) is linear.

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Q 25Q 25

A population changes with time.Its level after t years is given by the function .Over a certain period, the population is declining.What can be said about over this period?
A) is positive.
B) is negative.
C) is zero.
D) is linear.

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Q 26Q 26

A population changes with time.Its level after t years is given by the function .After a period of population increase, the population reaches a maximum value.What can be said about at this time?
A) is positive.
B) is negative.
C) is zero.
D) is linear.

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Q 27Q 27

A population changes with time.Its level after t years is given by the function .After a period of population decrease, the population reaches a minimum value.What can be said about at this time?
A) is positive.
B) is negative.
C) is zero.
D) is linear.

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