
Svetlana N.
asked 11/30/22In the year 2008 Apple sold 11 million iPhones. Over the next few years, annual sales increased by an average of 55%
In the year 2008 Apple sold 11 million iPhones. Over the next few years, annual sales increased by an average of 55%, which we will model using a geometric sequence with r = 1.55
Use the geometric summation formula Sn = a1 (1-r^n) / 1 - r, to estimate the total number of iPhones sold in the eight years spanning 2008 and 2015. Give your answer in millions of phones, rounded to one decimal place.
___________ million phones
1 Expert Answer
Joshua S. answered 11/30/22
9+ Years Experience in Math Grades 6-12, SAT/ACT Prep + College level
It is strange to me that the problem describes "the next few years" as a 7 year gap (my guess is that this question is part of a question bank with different values), but using this information we can find the sum of the geometric series.
The sales increased by an average of 55% over the course of 7 years, and this growth was exponential (not linear) since we are dealing with a geometric series. Thus, the rate of sales (per year) can be found by finding the 7th root of 1.55 (1.55 representing 55% growth over 7 years), which is approximately 1.0646. This is our r, or our growth in sales per year. To calculate Sn, we must find S7 since 2015 is seven years after 2008.
Sn = a1(1-rn) / (1 - r)
S7 = 11,000,000(1-(1.0646)7)/(1-(1.0646))
S7 = 11,000,000(1-1.55)/(1-(1.0646))
S7 = 11,000,000(-0.55)/(-0.0646)
S7 = 93,653,250.8
Rounding to the nearest million phones... 94 million phones.
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Peter R.
11/30/22