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?
Future Amount $=I(1+r)^t$
Round your answer to the nearest whole number.
Answer (2)
Identify the initial number of subscribers ( I = 576 ), the rate of increase ( r = 0.3 ), and the time period ( t = 3 years).
Substitute the values into the formula: Future Amount = 576 ( 1 + 0.3 ) 3 .
Calculate the future amount: Future Amount = 576 × ( 1.3 ) 3 = 1265.152 .
Round the 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. The formula for future amount is given as: Future Amount = I ( 1 + r ) t , where I is the initial amount, r is the rate of increase, and t is the time period.
Identifying the Given Values We are given the following values: Initial number of subscribers, I = 576 Rate of increase, r = 30% = 0.30 Time period, t = 3 years
Substituting the Values into the Formula Now, we substitute the given values into the formula: Future Amount = 576 ( 1 + 0.3 ) 3 Future Amount = 576 ( 1.3 ) 3 Future Amount = 576 × 2.197 Future Amount = 1265.152
Rounding to the Nearest Whole Number We are asked to round the answer to the nearest whole number. Therefore, the number of subscribers after 3 years is approximately 1265.
Examples
This type of calculation is useful in many real-world scenarios, such as predicting population growth, estimating the future value of investments, or determining the spread of a disease. For example, if a city has a population of 10,000 and the population grows by 5% each year, we can use this formula to predict the population in 10 years. Similarly, if you invest $1,000 in a savings account with an annual interest rate of 3%, you can calculate how much money you will have after 5 years. Understanding exponential growth is crucial in finance, biology, and urban planning.
After 3 years, the mobile carrier will have approximately 1265 subscribers, calculated using the exponential growth formula. The initial number of subscribers is 576, with an annual increase of 30%. Rounding the final figure leads to 1265 subscribers.
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