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Exponential growth can be modeled using the equation \( A = P e^{rt} \), where \( A \) is the accumulated value, \( P \) is the initial amount, \( r \) is the growth rate, and \( t \) is time. The table below demonstrates how the value evolves over time under continuous compounding, assuming a constant rate.
| Time (t) | Formula | Value (A) |
|---|---|---|
| 0 | \( 1 \cdot e^{0} \) | 1.00 |
| 2 | \( 1 \cdot e^{0.5 \times 2} \) | 2.72 |
| 4 | \( 1 \cdot e^{0.5 \times 4} \) | 7.39 |
| 6 | \( 1 \cdot e^{0.5 \times 6} \) | 20.09 |
| 8 | \( 1 \cdot e^{0.5 \times 8} \) | 54.60 |
| 10 | \( 1 \cdot e^{0.5 \times 10} \) | 148.41 |
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Q1 TRENDS
Live shares data
| ID | Name | Price |
|---|---|---|
| ABSA | Absa Bank Kenya Plc | 28.10 |
| ALP | ALP Real Estate Investment Trust | 1.00 |
| AMAC | Africa Mega Agricorp | 109.50 |
| ARM | ARM Cement Ltd | 5.50 |
| BAMB | Bamburi Cement Ltd | 54.00 |
| BAT | British American Tobacco Kenya | 569.00 |
| BKG | BK Group Plc | 54.50 |
| BOC | BOC Kenya Ltd | 150.25 |
| BRIT | Britam Holdings Ltd | 12.25 |
| CABL | East African Cables | 1.71 |
Live rates
| Currency Pair | Exchange Rate |
|---|---|
| USD/KES | 129.52 |
| GBP/KES | 175.59 |
| AUD/KES | 93.40 |
| EUR/KES | 151.90 |
| ZAR/KES | 7.87 |
Headline Content
Lebesgue measure generalizes length so that for an interval \( [a,b] \), the measure is \( m([a,b]) = b - a \). For any set \( E \subset \mathbb{R} \), its outer measure is defined by
\[ m^*(E) = \inf \left\{ \sum_{i=1}^{\infty} |I_i| : E \subset \bigcup_{i=1}^{\infty} I_i \right\}. \]
A set is measurable if it satisfies Carathéodory’s condition:
\[ m^*(A) = m^*(A \cap E) + m^*(A \cap E^c). \]