Exercise 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. </span>                 <h2>Exercise 2</h2>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.                 <h2>Exercise 3</h2>A car rental charge is100 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 <span class="actividades_g">miles</span> was travelled in one day, how much is the rental company going to receive as a payment?                 <h2>Exercise 4</h2>When digging into the earth, the temperature rises according to the following linear equation: t = 15 + 0.01 h. <strong>t</strong> is the increase in temperature in degrees and <strong>h</strong> is the depth in meters. Calculate:  <span class="numero_v">1.</span> What  the temperature will be at 100 m depth? <span class="numero_v">2.</span>Based on this equation, at what depth would there be a temperature of 100 ºC? <h2>Exercise 5</h2>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: <span class="numero_v">1.</span>The equation that relates <strong>y</strong> with <strong>t</strong>. <span class="numero_v">2.</span> The pollution level at 4 o'clock in the afternoon. <h2>Exercise 6</h2>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. <h2>Exercise 7</h2>For the function f(x)= ax + b, f(0) = 3 and f(1) = 4. <span class="numero_v">1. </span>Determine the coefficients that satisfy the equation: <span class="numero_v">2. </span>Write the equation and represent it graphically: <span class="numero_v">3. </span>Indicate the intervals where the function has a positive and negative value.                 </div>                  </section><section id="am" style="">                                                    <h2>Solution of exercise 1</h2>                 Three pounds of squid can be purchased at the market for18. Determine the equation and represent the function that defines the cost of squid based on weight.

18/3 = 6 y = 6x

Superprof

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 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

Solution of exercise 3

A car rental charge is 100 per day plus0.30 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

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 · 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

Solution of exercise 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

Solution of exercise 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

TimeCapacity
14
28
312
416
......

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 · 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

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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Bilal murtaza
Bilal murtaza
Guest
23 Sep.

Break even point

Bilal murtaza
Bilal murtaza
Guest
23 Sep.

I have math qstn problm