Question

The value y of a computer after its purchase is given by y(t)=3200-200t

Answer 1

Problem Statement

The question gives us an equation that gives us the value of a computer after its initial value at purchase. The equation given is:

`\begin{gathered} y(t)=3200-200t, \\ \text{where,} \\ t=years\text{ afer year of purchase} \\ y=\text{value of the computer} \end{gathered}`

We are asked to find:

a. The y-intercept and its meaning.

b. The slope and its meaning

Solution

To solve this question, we simply need to compare the equation given to the general slope-intercept equation. The general slope-intercept equation is given by:

`\begin{gathered} y(t)=mt+c \\ \text{where,} \\ c=y-\text{intercept} \\ m=\text{slope of the equation} \end{gathered}`

With this equation, we can compare with the equation given in the question:

`\begin{gathered} y=mt+c \\ y=3200-200t \\ \text{This implies that:} \\ \\ \text{slope(m)}=-200 \\ y-\text{intercept}=3200 \end{gathered}`

Thus, let us answer the questions:

a. The y-intercept and its meaning:

The y-intercept is 3200.

When we vary the time variable in the equation given, we can get a sense of what this y-intercept means. This is done below: