An author published a book which was being sold online. The first month the author sold 28500 books, but the sales were declining steadily at 14% each month. If this trend continues, how many total books would the author have sold over the first 16 months, to the nearest whole number? Answer:

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An author published a book which was being sold online. The first month the author sold 28500 books, but the sales were declining steadily at  14% each month. If this trend continues, how many total books would the author have sold over the first 16 months, to the nearest whole number? Answer:

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Identify initial number: Identify the initial number of books sold and the monthly percentage decline. Initial number of books sold (a) = 28500 Monthly decline rate (r) = 14% or 0.14Determine formula for total: Determine the formula for the total number of books sold over a period of time with a steady percentage decline. The total number of books sold over the first 16 months can be calculated using the formula for the sum of a geometric series: S_n = a(1 - r^n) / (1 - r) where S_n is the total number of books sold after n months, a is the initial number of books sold, r is the monthly decline rate, and n is the number of months.Substitute known values: Substitute the known values into the formula. a = 28500 r = 0.14 n = 16 S_16 = 28500(1 - 0.14^16) / (1 - 0.14)Calculate total number: Calculate the total number of books sold over the first 16 months. S_16 = 28500(1 - 0.14^16) / (1 - 0.14) First, calculate 0.14^16: 0.14^16 ≈ 0.000000074 Now, calculate 1 - 0.14^16: 1 - 0.000000074 ≈ 0.999999926 Next, calculate the denominator 1 - 0.14: 1 - 0.14 = 0.86 Finally, calculate the total sum S_16: S_16 ≈ 28500 * (0.999999926 / 0.86) S_16 ≈ 28500 * 1.1627907 S_16 ≈ 33125.99Round total number: Round the total number of books sold to the nearest whole number. S_16 ≈ 33126

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