Many nations compare the value of their currency to the US dollar. On a day early in 2009, $1 CDN (1 Canadian dollar) was worth $0.8290 USD (US dollar). This is known as an exchange rate. On the same date $1 USD could be used to buy 0.7579 Euros or 0.6709 UK pounds (United Kingdom pounds Sterling).

Question

Many nations compare the value of their currency to the US dollar. On a day early in 2009, $1 CDN (1 Canadian dollar) was worth $0.8290 USD (US dollar). This is known as an exchange rate. On the same date $1 USD could be used to buy 0.7579 Euros or 0.6709 UK pounds (United Kingdom pounds Sterling).

Demonstrate and explain how the above exchange rates could be used to create composite functions to convert Canadian dollars to Euros or UK pounds. (4 marks)

I am planning a trip to Portugal, Spain and France with a side trip to England. Using your composite functions, determine how many Euros I could get for $1000 CDN and how many UK pounds for $500 CDN. (2 marks)

Answer 1

To create composite functions to convert Canadian dollars to Euros or UK pounds, we can break down the process into two steps:

Step 1: Convert Canadian dollars to US dollars
Step 2: Convert US dollars to Euros or UK pounds

Step 1: Convert Canadian dollars to US dollars:
Given:
$1 CDN = $0.8290 USD

We can represent this conversion as a function, let's call it f:
f(CDN) = CDN * 0.8290 USD

Step 2: Convert US dollars to Euros or UK pounds:
Given:
$1 USD = 0.7579 Euros
$1 USD = 0.6709 UK pounds

For Euros, we can represent the conversion as a function, let's call it g:
g(USD) = USD * 0.7579 Euros

For UK pounds, we can represent the conversion as a function, let's call it h:
h(USD) = USD * 0.6709 UK pounds

Now, we can create the composite functions to convert Canadian dollars to Euros or UK pounds:

Composite function to convert Canadian dollars to Euros (CDN -> USD -> Euros):
F(CDN) = g(f(CDN))
F(CDN) = g(CDN * 0.8290 USD)
F(CDN) = (CDN * 0.8290 USD) * 0.7579 Euros

Composite function to convert Canadian dollars to UK pounds (CDN -> USD -> UK pounds):
G(CDN) = h(f(CDN))
G(CDN) = h(CDN * 0.8290 USD)
G(CDN) = (CDN * 0.8290 USD) * 0.6709 UK pounds

Now, let's calculate the conversions for your trip:

Conversion of $1000 CDN to Euros:
F(1000) = (1000 * 0.8290 USD) * 0.7579 Euros
F(1000) = 829 USD * 0.7579 Euros
F(1000) = 627.11 Euros

Conversion of $500 CDN to UK pounds:
G(500) = (500 * 0.8290 USD) * 0.6709 UK pounds
G(500) = 414.50 USD * 0.6709 UK pounds
G(500) = 277.71 UK pounds

Therefore, you could get 627.11 Euros for $1000 CDN and 277.71 UK pounds for $500 CDN.