Alexander has to travel a distance of $latex 1.53\times 10^4$ meters daily to work and back.

a) Write down the distance as a decimal number.

b) Write down the answer to a) correct to 2 significant figures.

c) Round off the answer to a) to the nearest 10000.

A currency exchange service exchanges 1 EUR into US dollars using a buy rate of 1.1992 and sell rate of 1.1799. If Sandra exchanges 500 USD to EUR:

a) How much EUR will she get?

b) If she changes the EUR back to USD, how much would she receive?

c) How much would the resultant commission be for a double transaction?

Consider the arithmetic sequence defined by $latex u_{n}=5n+3$.

a) Find the common difference d.

b) Find $latex u_{1} $ and $latex u_{37} $.

c) For what values of $latex n$ are the terms in the sequence smaller than 150?

Stefan has an ant farm. He started out with 20 ants. The ant population is increasing by 50% each month.

a) How many ants will there be after one year?

b) After how many months will the ant farm reach a population of 5000 ants?

Gemma wants to buy a house worth $300000 in 5 years from now. Her bank account has an interest rate of 4.5% p.a. compounded monthly. How much does she need to deposit in order to be able to buy the house in 5 years from now?