A mobile carrier in a city has 576 subscribers. If the number of subscribers increases by 30% every year, how many subscribers will there be after 3 years?
[tex]Future Amount =I(1+r)^t[/tex]
Round your answer to the nearest whole number.
Answer (2)
Identify the initial number of subscribers, the annual increase rate, and the time period.
Substitute the values into the formula: Future Amount = I ( 1 + r ) t .
Calculate the future amount: Future Amount = 576 × ( 1 + 0.30 ) 3 = 1265.152 .
Round the calculated future amount to the nearest whole number: 1265 .
Explanation
Understanding the Problem We are given that a mobile carrier has 576 subscribers and the number of subscribers increases by 30% every year. We want to find the number of subscribers after 3 years. We are also given the formula for future amount: Future Amount = I ( 1 + r ) t , where I is the initial amount, r is the rate of increase, and t is the time in years.
Identifying Given Values We are given: Initial number of subscribers, I = 576 Annual increase rate, r = 30% = 0.30 Time period, t = 3 years
Substituting Values into the Formula We substitute the values of I , r , and t into the formula: Future Amount = I ( 1 + r ) t .
Calculating the Future Amount Future Amount = 576 × ( 1 + 0.30 ) 3 Future Amount = 576 × ( 1.3 ) 3 Future Amount = 576 × 2.197 Future Amount = 1265.152
Rounding to the Nearest Whole Number We round the calculated future amount to the nearest whole number. Future Amount ≈ 1265
Final Answer Therefore, after 3 years, there will be approximately 1265 subscribers.
Examples
This type of calculation is useful in many real-world scenarios, such as predicting population growth, estimating the value of investments, or determining the spread of a disease. For example, a city planner might use this formula to predict the population of a city in 10 years, given the current population and the annual growth rate. Similarly, an investor might use this formula to estimate the future value of an investment, given the initial investment and the annual rate of return. Understanding exponential growth is crucial in making informed decisions in various fields.
Using the formula for exponential growth, we calculated that after 3 years, the mobile carrier will have approximately 1265 subscribers. The initial number of subscribers is 576, and with a 30% annual increase, we found the future amount by applying the growth rate over the specified time period. The final answer, rounded to the nearest whole number, is 1265 subscribers.
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