Mathematics 30 June 1999 Grade 12 Diploma Exam
Mathematics 30 June 1999 Grade 12 Diploma Exam
Mathematics 30 June 1999 Grade 12 Diploma Exam
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Use the following information to answer the next question.<br />
A sports store is planning a sales promotion of mountain bikes. Each day that<br />
a bike remains unsold, the price will be discounted by 2% of the previous<br />
day’s price. The table below gives the successive daily prices of a mountain<br />
bike with an original price of $1 224.49.<br />
Day<br />
Bike Price<br />
1 $1 200.00<br />
2 $1 176.00<br />
3 $1 152.48<br />
4 $1 <strong>12</strong>9.43<br />
5 $1 106.84<br />
Written Response—10%<br />
1. Successive daily prices of the mountain bike can be approximated by using the<br />
recursive formula t 1<br />
= $1 200.00 and t n + 1<br />
= 0.98t n<br />
.<br />
• Determine the price of the mountain bike on day 8 of this sales promotion.<br />
A POSSIBLE SOLUTION<br />
t 5 + 1<br />
= 0.98(1 106.84) = 1 084.70<br />
t 6 + 1<br />
= 0.98(1 084.70) = 1 063.00<br />
t 7 + 1<br />
= 0.98(1 063.00) = 1 041.75<br />
On the 8 th of the sales promotion the cost of the bike is $1 041.75.<br />
• Write an expression for t n<br />
as a function of n, n ∈ N.<br />
A POSSIBLE SOLUTION<br />
t 1<br />
= 1 200.00<br />
t 2<br />
= 0.98(1 200.00) hence r = 0.98<br />
t n<br />
= 1 200(0.98) n – 1 , n ∈ N<br />
4
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