Question

A shipping company's inventory for a given item is modeled by the function f(x) = 500 − 8x, where "x" is the number of hours that elapse since opening. Explain the contextual meaning of the coefficient of x and write a function g(x) to model tomorrow's inventory if the company ships for ten hours today, no new inventory arrives, and the shipping rate doubles.

Answer 1

See step by step explanation.

Explanation:

1. The coefficient of x means there are 8 item shipped every hour.

2. g(x) = 500 - f(10) - 16x = 420 - 16x

Answer 2

The coefficient of x is -8 it means the company ships 8 items each hour.

`g(x)=420-16x`

Explanation:

The given function is

`f(x)=500-8x`

where, "x" is the number of hours that elapse since opening.

In the given function 500 represents the initial inventory and coefficient of x represent rate of shipping per hour.

The coefficient of x is -8 it means the company ships 8 items each hour.

It the company ships for ten hours today, then the initial inventory for tomorrow is

`f(x)=500-8(10)=420`

The shipping rate doubles. So, the shipping rate for tomorrow is

`2* (-8)=-16`

The function g(x) to model tomorrow's inventory is

`g(x)=420-16x`

Therefore, the required function is g(x)=420-16x.