Homework 3: Business Arithmetic 1, Indices and Logarithms
    Your score:          
Q1) The following are details of the charges from two telephone companies:  
  Company A charges a fixed amount of £ 25 per month and gives 120 minutes worth of free calls.
  For anything over the 120 minutes, calls are charged at 3 pence per minute.
  Company B has a fixed cost of £15, offers 60 minutes of free calls and charges 8 pence for each minute over 60.
  a) Find the monthly bill for a user who makes 150 minutes worth of calls:    
    with company A            
    with company B            
  b) How many minutes worth of calls have been made with company A    
    if the bill is £38.80?    
  Company B offers a discount of 6% to those customers who pay their bill online.
  c) Leia decides to pay her bill online. What would be her new bill for    
    making 150 minutes worth of calls? Answer to 2 decimal places.    
  d) If m minutes worth of calls are made per month, write an expression for the   
    total cost c in pounds for each company (ignoring any online discounts).  
    A: c =      for m < 120  
    c = m   +  for m 120  
    B: c =      for m < 60  
    c = m   +  for m 60  
  e) Find the number of minutes used for which the bill from both companies would be equal:
    (Ignore any online discounts.)
      number of minutes: rounded to nearest minute.    
      cost of bill:          
Q2) Andrea's company makes chocolate animals sold in boxes of 12. Each animal is made from 16g of chocolate.
  The empty boxes cost £ 0.20 each and 1 kg of chocolate costs £ 25.
  a) How many chocolate animals can be made from 1 kilogram of chocolate?    
  b) How many boxes can she fill with chocolate animals?      
  c) What are her total costs making this many boxes given she bought 1 kg of chocolate?
  d) She sells boxes for £ 6.50 each, what is her percentage profit margin?
  e) How much should she sell each box for to have a profit margin of 25% ?
Q3)  A car rental company and decides to offer two types of tarrif:
    Tarrif A: No fixed fee but a charge of £ 1.40 per mile travelled.      
    Tarrif B: A fixed fee of £250 plus £0.12 per mile travelled.      
  For both tarrifs, the customer must also pay £0.65 per mile for petrol.
  a) If a customer travels 380 miles, calculate the cost under each tarrif:  
    Cost under tarrif A:            
    Cost under tarrif B:            
  b) Let x be the number of miles travelled and let y be the total cost.  
  Write down an expression for y in terms of x for each tarrif:  
    A y = x   +        
    B y = x   +        
  c) The total cost is the same for both tariffs, find:          
  i) the number of miles travelled:          
  ii) the total cost:          
Q4) a) VAT at 19.5% is added to the price of all goods. If a digital radio is £ 105.10
  before the VAT is added, what is its price after the VAT is added?
  b) Celia bought an oven for £650. The price included the VAT.
  What was the price of the oven before the VAT was added?
Q5) The value of an investment fund is given by the equation V = 8400 (1.032)n  
  where n is the number of years after the initial investment.  
  a) What is the value of the initial investment?  
  b) How long until the investment is worth £12,000? years
  c) How long until the investment triples in value? years
Q6) Express (1/2) log464 x14 2 log44 x2 + 3 in the form log4( a x b)  
      log   x