L i ne a r Funct i o n Wo r d Pr o b le ms
1Three
pounds of squid can be purchased at the market for $18. Determine the
equation and represent the function that defines the cost of squid based on weight.
2It
has been observed that a particular plant's growth is directly proportional to
time. It measured 2 cm when it arrived at the nursury and 2.5 cm exactly one week
later. If the plant continues to grow at this rate, determine the function that represents
the plant's growth and graph it.
3A
car rental charge is $100 per day plus $0.30 per mile travelled. Determine the
equation of the line that represents the daily cost by the number of miles travelled and
graph it. If a total of 300 miles was travelled in on e day, how much is the rental
company going to receive as a payment?
4When
digging into the earth, the temperature rises according to the following
linear equation:
t = 15 + 0.01 h.
t is the increase in temperature in degrees and h is the depth in meters. Calculate:
1. What the temperature will be at 100 m depth?
2.Based on this equation, at what depth would there be a temperature of 100 ºC?
5The
pollution level in the centre of a city at 6 am is 30 parts per million and it
grows in linear fashion by 25 pa rts per million every hour. If y is pollution and t is time
elapsed after 6 am, determine:
1.The equation that relates y with t.
2. The pollution level at 4 o'clock in the afternoon.
6A
faucet dripping at a constant rate fills a test tube with 0.4 cm³ of water every
minute. Form a table of values for time and capacity, determine the equation and
represent it graphically.
7For
the function f(x)= ax + b, f(0) = 3 and f(1) = 4.
1. Determine the coefficients that satisfy the equation:
2. Write the equation and represent it graphically:
3. Indicate the intervals where the function has a positive and negative value.
1
Three pounds of squid can be purchased at the market for $18. Determine the
equation and represent the function that defines the cost of squid based on weight.
18/3 = 6 y = 6x
2
It has been observed that a particular plant's growth is directly proportional to
time. It measured 2 cm when it arrived at the nursury and 2.5 cm exactly one week
later. If the plant continues to grow at this rate, determine the function that represents
the plant's growth and graph it.
Initial height = 2 cm
Weekly growth = 2.5 − 2 = 0.5
y= 0.5 x + 2
3
A car rental charge i s $100 per day plus $0.30 per mile travelled. Determine the
equation of the line that represents the daily cost by the number of miles travelled and
graph it. If a total of 300 miles was travelled in one day, how much is the rental
company going to receive as a payment?
y = 0.3 x +100
y = 0.3 · 300 + 100 = $190
4
When digging into the earth, the temperature rises according to
the following
linear equation:
t = 15 + 0.01 h.
t is the increase in temperature in degrees and h is the depth in meters. Calculate:
1. What the temperature will be at 100 m depth?
t = 15 + 0.01 · 100 = 16 ºC
2.Based on this equation, at what depth would there be a temperature of 100 ºC?
100 = 15 + 0.01 h = 8,500 m
5
The pollution level in the centre of a city at 6 am is 30 parts per million and it
grows in linear fashion by 25 parts per million every hour. If y is pollution and t is time
elapsed after 6 am, determine:
1.The equation that relates y with t.
y = 30 + 25t
2. The pollution level at 4 o'clock in the afternoon.
10 hours have elapsed between 6 in the morning to four in the afternoon.
f(10) = 30 + 25 · 10 = 280
6
A faucet dripping at a constant rate fills a test tube with 0.4 cm³ of water every
minute. Form a table of values for time and capacity, determine the equation and
represent it graphically.
y =0.4 x
Time
Capacity
1
4
2
8
3
12
4
16
...
...
7
For the function f(x)= ax + b, f(0) = 3 and f(1) = 4.
1. Determine the coefficients that satisfy the equation:
f(0) = 3
3 = a · 0 + b b = 3
f(1) = 4.
4 = a · 1 + b a = 1
2. Write the equation and represent it graphically:
f(x) = x + 3
3. Indicate the intervals where the function has a positive and negative value.
x + 3 = 0 x = − 3
f(−4) = −1 < 0f(0) = 3 > 0
f(x) < 0 if x< −3
f(x) > 0 if x> −3