Question

- Show all the steps of your working and give your reasons clearly. Give a proper conclusion to your answers where applicable. Question 1 Write the repeating decimal number 3,142 as an improper fraction. Question 2 2.1 A father is four times as old as his daughter. In 6 years he will be three times as old as she is then. How old is the daughter now? 2.2 The distance between two towns $ A $ and $ B $, is $ 90 \mathrm{~km} $. John cycles from $ A $ to $ B $ whereas Harry cycles from $ B $ to $ A $. They start cycling towards cach other at the same time. John cycles twice as fast as Harry does. If they meet 2 hours later, at what average speed is each cyclist traveling? (8) 2.3 The area covered by water weed on a dam increases exponentially according to the formula \[ A=A_{0} e^{k t}, \] where $ A $ is the area, in square metres, covered by weed after $ t $ days. The initial area $ A_{0} $ of water weed is $ 200 \mathrm{~m}^{2} $. After 10 days the area is $ 300 \mathrm{~m}^{2} $. (a) Determine the value of $ k $. Leave your answer in terms of $ \ln $. (b) Use the formula above, and the value of $ k $ in terms of $ \ln $, to determine the area covered by water weed after 30 days. $ [23] $

          - Show all the steps of your working and give your reasons clearly. Give a proper conclusion to your answers where applicable.

Question 1
Write the repeating decimal number 3,142 as an improper fraction.
Question 2
2.1 A father is four times as old as his daughter. In 6 years he will be three times as old as she is then. How old is the daughter now?
2.2 The distance between two towns \( A \) and \( B \), is \( 90 \mathrm{~km} \). John cycles from \( A \) to \( B \) whereas Harry cycles from \( B \) to \( A \). They start cycling towards cach other at the same time. John cycles twice as fast as Harry does. If they meet 2 hours later, at what average speed is each cyclist traveling? (8)
2.3 The area covered by water weed on a dam increases exponentially according to the formula
\[
A=A_{0} e^{k t},
\]
where \( A \) is the area, in square metres, covered by weed after \( t \) days. The initial area \( A_{0} \) of water weed is \( 200 \mathrm{~m}^{2} \). After 10 days the area is \( 300 \mathrm{~m}^{2} \).
(a) Determine the value of \( k \). Leave your answer in terms of \( \ln \).
(b) Use the formula above, and the value of \( k \) in terms of \( \ln \), to determine the area covered by water weed after 30 days.
\( [23] \)

$- Show all the steps of your working and give your reasons clearly. Give a proper conclusion to your answers where applicable. Question 1 Write the repeating decimal number 3,142 as an improper fraction. Question 2 2.1 A father is four times as old as his daughter. In 6 years he will be three times as old as she is then. How old is the daughter now? 2.2 The distance between two towns A and B, is 90 km. John cycles from A to B whereas Harry cycles from B to A. They start cycling towards cach other at the same time. John cycles twice as fast as Harry does. If they meet 2 hours later, at what average speed is each cyclist traveling? (8) 2.3 The area covered by water weed on a dam increases exponentially according to the formula A=A0 e^k t, where A is the area, in square metres, covered by weed after t days. The initial area A0 of water weed is 200 m^2. After 10 days the area is 300 m^2. (a) Determine the value of k. Leave your answer in terms of ln. (b) Use the formula above, and the value of k in terms of ln, to determine the area covered by water weed after 30 days. [23]$

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