Question

A computer can sort x objects in t seconds, as modeled by the function

below:
t=0.007x2 + 0.003x
How many objects are required to keep the computer busy for exactly 9
seconds?
Round to the nearest whole object.

Answer 1

36

Explanation:

Answer 2

36 objects

Explanation:

You want the value of x when t=9, so you're solving ...

9 = 0.007x^2 +0.003x

9 = 0.007(x^2 + 3/7x)

From here, we observe that an approximation is probably sufficient.

9/0.007 = x(x +3/7) . . . . . the expression on the right is nearly x^2

x ≈ 3/√.007 ≈ 35.9 ≈ 36

We can check:

.007(36)(36 3/7) = 9.18

.007(35)(35 3/7) = 8.68

To keep the computer busy for 9 seconds, it needs to sort 36 objects.