Subjects algebra

Subscriber Growth

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1. **State the problem:** We need to find the number of new mobile phone subscribers by 2025 for all regions excluding APAC and MENA, assuming current growth rates continue. 2. **Identify the regions to consider:** CIS, Europe, Latin America, North America, Sub-Saharan Africa. 3. **Calculate the growth rate for each region from 2016 to 2020:** For each region, growth rate $r = \frac{\text{subscribers in 2020} - \text{subscribers in 2016}}{\text{subscribers in 2016}}$. - CIS: $r = \frac{239 - 223}{223} = \frac{16}{223} \approx 0.0717$ - Europe: $r = \frac{473 - 455}{455} = \frac{18}{455} \approx 0.0396$ - Latin America: $r = \frac{521 - 453}{453} = \frac{68}{453} \approx 0.1501$ - North America: $r = \frac{315 - 292}{292} = \frac{23}{292} \approx 0.0788$ - Sub-Saharan Africa: $r = \frac{543 - 427}{427} = \frac{116}{427} \approx 0.2717$ 4. **Calculate the annual growth rate assuming linear growth over 4 years (2016 to 2020):** Annual growth rate $a = \frac{r}{4}$ - CIS: $a = 0.0717 / 4 = 0.0179$ - Europe: $a = 0.0396 / 4 = 0.0099$ - Latin America: $a = 0.1501 / 4 = 0.0375$ - North America: $a = 0.0788 / 4 = 0.0197$ - Sub-Saharan Africa: $a = 0.2717 / 4 = 0.0679$ 5. **Calculate the number of subscribers in 2025 (5 years after 2020) using linear growth:** Subscribers in 2025 $= \text{subscribers in 2020} \times (1 + 5 \times a)$ - CIS: $239 \times (1 + 5 \times 0.0179) = 239 \times 1.0895 = 260.4$ - Europe: $473 \times (1 + 5 \times 0.0099) = 473 \times 1.0495 = 496.4$ - Latin America: $521 \times (1 + 5 \times 0.0375) = 521 \times 1.1875 = 618.3$ - North America: $315 \times (1 + 5 \times 0.0197) = 315 \times 1.0985 = 345.1$ - Sub-Saharan Africa: $543 \times (1 + 5 \times 0.0679) = 543 \times 1.3395 = 727.3$ 6. **Calculate the increase in subscribers from 2020 to 2025 for each region:** - CIS: $260.4 - 239 = 21.4$ - Europe: $496.4 - 473 = 23.4$ - Latin America: $618.3 - 521 = 97.3$ - North America: $345.1 - 315 = 30.1$ - Sub-Saharan Africa: $727.3 - 543 = 184.3$ 7. **Sum the increases:** $21.4 + 23.4 + 97.3 + 30.1 + 184.3 = 356.5$ million new subscribers 8. **Compare with given options:** The closest option to 357 million is 360 million. **Final answer:** 360 million new subscribers excluding APAC and MENA by 2025.