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)
To convert Canadian dollars (CAD) to Euros or UK pounds using the given exchange rates, we can use composite functions. Let's call the CAD to USD exchange rate as f(x), where x represents the amount in CAD. Similarly, let's call the USD to Euro exchange rate as g(x) and the USD to UK pound exchange rate as h(x).
1. To convert CAD to Euros:
- Start with the amount in CAD (x).
- Convert the CAD to USD using the exchange rate f(x).
- The result of this conversion will give you the amount in USD.
- Then, convert the USD to Euros using the exchange rate g(x).
Using composite function notation, the conversion from CAD to Euros can be represented as g(f(x)).
2. To convert CAD to UK pounds:
- Start with the amount in CAD (x).
- Convert the CAD to USD using the exchange rate f(x).
- The result of this conversion will give you the amount in USD.
- Then, convert the USD to UK pounds using the exchange rate h(x).
Using composite function notation, the conversion from CAD to UK pounds can be represented as h(f(x)).
So, to summarize:
- CAD to Euros: g(f(x))
- CAD to UK pounds: h(f(x))
By plugging in the desired amount in CAD (x) into the composite functions, you can calculate the equivalent amount in Euros or UK pounds.