Resources

Resources

Write linear functions: word problems

Ping's Ice Cream Palace offers a special sundae that contains over

2

kilograms of ice cream plus any number of toppings.

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Write an inequality that describes

k

, the weight of the special sundae in kilograms.

Igbo uploaded a funny video of his cat onto a website.

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The relationship between the elapsed time,

d

, in days, since the video was first uploaded, and the total number of views,

V(d)

, that the video received is modeled by the following function.

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V(d)=10^{1.5 d}

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How many days will it take for the video to receive

1,000,000

views? Round your answer, if necessary, to the nearest hundredth.

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A bank efficiency ratio is the ratio of a bank's expenses to its revenue, expressed as a percentage. If a bank has

\$ 222

million dollars in expenses and an efficiency ratio of

75 \%

, what is its revenue in millions of dollars?

100-10 m

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Dante's goal this year is to read

100

books. The expression above models the number of books Dante has left to read

m

months after the beginning of the year. Based on the expression, how many books does Dante have left to read after

4

20 l+25 g-10

gives the number of dollars that Josie makes from mowing

l

lawns and raking

g

gardens. How many dollars does Josie make from raking

4

gardens and mowing

3

The administrators of a factory modeled the cumulative average construction time in minutes per engine component as a function of the total number of components their employees had previously constructed,

n

, using the following function:

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T(n)=3.5+7 \cdot 0.9^{n}

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What was the cumulative average time, in minutes, for an employee to construct one engine component when they first began?

The equation models the height,

h

, in feet above the water for a cable in a suspension bridge at a horizontal distance,

x

, in feet from the beginning of the span.

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h=0.0002(x-1,955)^{2}+100

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How many feet above the water is the lowest point on the cable?

Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window.

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H

represents the height of the tree (in centimeters),

t

years since Renata moved in.

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H=210+33 t

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How fast does the tree grow?

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centimeters per year

Harry took a loan from the bank.

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D

represents Harry's remaining debt (in dollars) after

t

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D=-200 t+9000

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What was the size of Harry's loan?

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\$

Anumeha mows lawns. She charges an initial fee and a constant fee for each hour of work.

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F

represents Anumeha's fee (in dollars) for working

t

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F=6+12 t

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How much does Anumeha charge for each hour of work?

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\$

D=-200 t+9000

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Harry took a loan from the bank. Each month, he pays a fixed amount of money back to the bank. The given equation shows the remaining amount of the loan,

D

, measured in dollars, after

t

months. How much does Harry pay back to the bank each month, in dollars?

0.2 B+0.1 S=C

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Rhia is using the given equation to investigate the carbon footprint,

C

, in kilograms of carbon dioxide (

\mathrm{CO}_{2}

) emissions, for her morning commute, during which

S

miles are by subway and

B

miles are by bus. How many kilograms of

\mathrm{CO}_{2}

per mile does the bus portion contribute to Rhia's carbon footprint?

l=510-42 t

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The old road length,

l

, in meters, after

t

hours of milling is given by the equation. How many meters of old road are removed for each hour of milling?

V=-2.6+\frac{d}{3}

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The electric potential,

V

, in volts, between two metal plates a distance of

d

millimeters from the left plate is given by the equation when

0 \leq d \leq 15

. By how many millimeters does the distance from the left plate increase for the potential to increase by

1

A boat must carry aluminum pieces for a construction project that weigh, in total, no more than

50

000

(\mathrm{kg})

. Each aluminum piece is either a beam, which weighs

100 \mathrm{~kg}

, or a connector plate, which weighs

2 \mathrm{~kg}

. If the boat is carrying the maximum weight of aluminum pieces, which of the following gives the number of beams,

b(c)

, as a function of the number of connector plates,

c

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1

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b(c)=500-0.02 c

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b(c)=25,000-50 c

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b(c)=50,000-100 c

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b(c)=50,000-2 c

P=\frac{2}{5} m+1.5

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P

, in dollars, of a train ticket used to travel a distance of

m

miles is given by the equation. By how many miles does the traveling distance increase if the ticket price increases by

1

C=0.25(L-1200)

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C

, in dollars, to the holder of a liability insurance account given a total liability of

L

dollars is given by the equation as long as

C

is positive. By how many dollars does the liability increase when the cost to the holder increases by

1

A teacher purchased

300

colored pencils for an upcoming project. The pencils she ordered come in packs of

20

30

14

packs in all. Write a system of equations to find the number of

20

(x)

30

(y)

the art teacher ordered.

Tom bought a boat for

\$3,000

and incurs a daily storage fee of

\$15

. Write a linear function to represent the total amount Tom will owe,

p(x)

x

days to pick it up.

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Krysta wants to take piano lessons. She asked a teacher how many new pieces she could expect to learn each month. The teacher gave an estimate of

3

. Write an equation that shows how the total number of pieces Krysta would learn,

y

, depends on the number of months of piano lessons,

x

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y