Tutorial 2

Questions for in-class tutorial:

Basic Maths:

1. Solve the following equations

a) 38 + 12e-0.5t = 208

b) ln(t + 3) = 4.2

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

25 + 23 + 21 + —— = 88

Application Questions:

1. 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

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

y=Ae^(-at)

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

Questions for self-study

1. Simplify the following expressions to a single term:

a) 3log(x) + log (10/x)- 2log(10x)

b)

2. Solve the following equation

a) et = 7 – 2et

b) 80 = 25 +(1.5)x

c) = 3.5

3. 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

4. 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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