June 26, 2019

Chapters

## Exercise 1

Three pounds of squid can be purchased at the market for 100 per day plus 18. Determine the equation and represent the function that defines the cost of squid based on weight.

18/3 = 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 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 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

## 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

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 · 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**

Break even point

I have math qstn problm