Exercise 1

Three pounds of squid can be purchased at the market for 18 dollars. Determine the equation and represent the function that defines the cost of squid based on weight.

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Exercise 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 nursery 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.

Exercise 3

A car rental charge is 100 dollars per day plus 0.30 dollars 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?

Exercise 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?

2.Based on this equation, at what depth would there be a temperature of { 100 }^{ \circ }C?

Exercise 5

The pollution level in the centre of a city at 6 am is 30ppm (parts per million) and it grows in a linear fashion by 25ppm (parts per million) every hour. If y is pollution and t is the 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.

Exercise 6

A faucet dripping at a constant rate fills a test tube with 0.4 { cm }^{ 3 } of water every minute. Form a table of values for time and capacity, determine the equation and represent it graphically.

Exercise 7

For 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.

 

Solution of exercise 1

Three pounds of squid can be purchased at the market for 18 dollars. Determine the equation and represent the function that defines the cost of squid based on weight.

Since it is a directly proportional question hence, y = kx:

y = 18, \quad x = 3

18 = k(3)

k = 6

y = 6x

 

Solution of exercise 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 nursery 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

 

Solution of exercise 3

A car rental charge is 100 dollars per day plus 0.30 dollars 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 \times 300) + 100 = 190 dollars

 

Solution of exercise 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 \times 100 = { 16 }^{ \circ }C

2.Based on this equation, at what depth would there be a temperature of { 100 }^{ \circ }C?

100 = 15 + 0.01h = 8,500 m

 

Solution of exercise 5

The pollution level in the centre of a city at 6 am is 30ppm (parts per million) and it grows in a linear fashion by 25ppm (parts per million) every hour. If y is pollution and t is the 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 \times 10 = 280

 

Solution of exercise 6

A faucet dripping at a constant rate fills a test tube with 0.4 { cm }^{ 3 } 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
... ...

 

Solution of exercise 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 \times 0 + b \qquad b = 3

f(1) = 4

4 = a \times 1 + b \qquad 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 \qquad x = -3

f(-4) = -1 < 0 \qquad f(0) = 3 > 0

f(x) < 0 \qquad if \quad x < -3

f(x) > 0 \qquad if \quad x > -3

 

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Hamza

Hi! I am Hamza and I am from Pakistan. My hobbies are reading, writing and playing chess. Currently, I am a student enrolled in the Chemical Engineering Bachelor program.