To determine what [tex]\( f(10) \)[/tex] represents, let's first evaluate the function [tex]\( f(x) = 10 + 20x \)[/tex] at [tex]\( x = 10 \)[/tex].
1. Substitute [tex]\( x = 10 \)[/tex] into the function:
[tex]\[
f(10) = 10 + 20 \cdot 10
\][/tex]
2. Calculate the value:
[tex]\[
f(10) = 10 + 200 = 210
\][/tex]
Now we know that [tex]\( f(10) = 210 \)[/tex]. Next, we need to interpret what this value represents. The function [tex]\( f(x) = 10 + 20x \)[/tex] appears to calculate a cost in dollars. Specifically, [tex]\( f(x) \)[/tex] gives the total cost for renting a bike for [tex]\( x \)[/tex] hours.
- The 10 appears to be a fixed cost.
- The term [tex]\( 20x \)[/tex] suggests that each hour costs 20 dollars.
Evaluating [tex]\( f(10) \)[/tex], we found that after 10 hours, the cost amounts to 210 dollars.
Now let's match this result with the given options:
a. The number of miles the bike can travel for a cost of \[tex]$10.
b. The number of miles the bike travels in 10 hours.
c. The number of hours the bike can be rented for a cost of \$[/tex]10.
d. The number of dollars it costs to rent the bike for 10 hours.
Option d, "The number of dollars it costs to rent the bike for 10 hours," accurately describes the meaning of [tex]\( f(10) \)[/tex]. The function output [tex]\( f(10) = 210 \)[/tex] means that renting the bike for 10 hours would cost 210 dollars.
Therefore, the correct answer is:
d. The number of dollars it costs to rent the bike for 10 hours.
