To determine how long it will take the computer to sort 10 objects, we will use the given function:
[tex]\[
t = 0.005 x^2 + 0.002 x
\][/tex]
where [tex]\( x \)[/tex] is the number of objects, and [tex]\( t \)[/tex] is the time in seconds it takes to sort [tex]\( x \)[/tex] objects.
1. Substitute [tex]\( x = 10 \)[/tex] into the function:
[tex]\[
t = 0.005 (10)^2 + 0.002 (10)
\][/tex]
2. Calculate [tex]\( (10)^2 \)[/tex]:
[tex]\[
(10)^2 = 100
\][/tex]
3. Substitute and simplify:
[tex]\[
t = 0.005 \times 100 + 0.002 \times 10
\][/tex]
[tex]\[
t = 0.5 + 0.02
\][/tex]
4. Add the terms:
[tex]\[
t = 0.52
\][/tex]
So, the time [tex]\( t \)[/tex] taken to sort 10 objects is [tex]\( 0.52 \)[/tex] seconds.
5. Round to the nearest hundredth:
[tex]\[
0.52 \text{ seconds}
\][/tex]
Thus, it will take the computer 0.52 seconds to sort 10 objects.
