Let's break down the problem step-by-step to find the total number of sales on January 1, 2025, given the function [tex]\( f(x) = 17,281 \cdot (1.031)^x \)[/tex].
1. Understand the given function:
The function [tex]\( f(x) = 17,281 \cdot (1.031)^x \)[/tex] represents the total number of sales in terms of [tex]\( x \)[/tex], where [tex]\( x \)[/tex] is the number of years after the initial measurement date of January 1, 2013.
2. Determine [tex]\( x \)[/tex]:
To find the total number of sales on January 1, 2025, we need to determine the value of [tex]\( x \)[/tex] for this date.
January 1, 2025, is 12 years after January 1, 2013. Therefore, [tex]\( x = 12 \)[/tex].
3. Substitute [tex]\( x \)[/tex] into the function:
We substitute [tex]\( x = 12 \)[/tex] into the function [tex]\( f(x) = 17,281 \cdot (1.031)^x \)[/tex].
4. Calculate the total number of sales:
We perform the calculation:
[tex]\[
f(12) = 17,281 \cdot (1.031)^{12}
\][/tex]
Using the given result, we find:
[tex]\[
17,281 \cdot (1.031)^{12} \approx 24,927.163
\][/tex]
5. Round to the nearest whole number:
The total number of sales is approximately 24,927.163, which we round to the nearest whole number.
Therefore, the total number of sales on January 1, 2025, will be approximately 24,927 books.
Final Answer: 24,927 books
