Question

The worldwide number (in millions) of a particular phone sold can be approximated by the function f(x) = - 879 + 404 Inx, where x = 11 corresponds to 2011.

(a) What was the number of worldwide sales for the particular phone in 2013?
(b) If the model continues to be accurate, what was the first full year in which the particular
phone sales exceed 275 million?
(a) To find the number of worldwide sales in 2013, substitute 11 for x in the function.
(Simplify your answer.)
The number of worldwide sales for the particular phone in 2013 was approximately million
(Type an integer or decimal rounded to the nearest tenth as needed.)
(b) The first full year in which the particular phone sales exceed 275 million is I.

Answer 1

(a) 157 million

(b) 2018

Explanation:

(a) Since x=11 corresponds to the year 2011, we presume that x is 'years after 2000', and that for 2013, we need to use x=13.

f(13) = -879 +404·ln(13) ≈ 157.24

About 157 million phones were sold in 2013.

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(b) To find the year that sales exceeded 275 million, we solve ...

f(x) = 275

-879 +404·ln(x) = 275

404·ln(x) = 1154

ln(x) = 1154/404

x = e^(1154/404) ≈ 17.399

Sales will first exceed 275 million in 2017. The first full year in which sales are over 275 million is 2018.