**Tutorial 2**

**Questions for in-class tutorial:**

**Basic Maths:**

- Solve the following equations
- a) 38 + 12e
^{-0.5t}= 208 - b) ln(t + 3) = 4.2

- How many terms of the following series must be added to give the sum indicated?

25 + 23 + 21 + —— = 88

**Application Questions:**

- A rural population (given in thousands) is projected to decline according to the equation

P = 15e^{-0.1t}. If t = 0 at the beginning of 2008:

- a) calculate the numbers in the population at the beginning of 2010 and 2016
- b) calculate the number of years it will take for the population to decline to 10000

- The value of a second-hand car reduces exponentially with age, so that its value $y after years can be modelled by the formula:

If the car was worth $50000 when new and $38000 after two years, find the values of and α. Use this model to predict the value of the car when the car if five years old.

** **

**Questions for self-study**

- Simplify the following expressions to a single term:
- a) 3log(x) + log ( – 2log(10x)
- b)

- Solve the following equation
- a) e
^{t}= 7 – 2e^{t} - b) 80 = 25 +(1.5)
^{x} - c) = 3.5

- A company manufacturers deckchairs for a 10-week period each year. Production starts with 600 chairs in week 1 and increases by 50 for each subsequent week. Use series to calculate:
- a) The number of chairs manufactured in week 7
- b) The total number of chairs manufactured during the 10 weeks

- Two competing companies produce mobile phones. Company A starts production at 1000 phones per week and plans to increase output by 200 each week. Company B starts production with 500 phones per week and plans to increase output by 20% each week.
- a) calculate the weekly production in weeks 5 and 10 for each firm
- b) calculate the total production during the first 15 weeks for each firm

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