Question

A computer manufacturer releases a new laptop model. The total sales of this computer can be modeled by the function S(t)=75/1+52e^(-0.8t), where S(t) is measured in thousands of computers.

What is the number of sales the manufacturer can expect its sales to stabilize to over time?

Answer 1

Answer:

The number for the stable sale is 75,000.

Step-by-step explanation:

We are given that,

The total sales of the computer over time is modeled by,

$S(t)=\frac{75}{1+52e^{-0.8t}}$ (in thousands).

It is required to stabilize the number of sales over time.

Now we can see that,

As $t\rightarrow \infty$, the value $52e^{-0.8t}\rightarrow 0$

So, for large values of t, S(t)= 75,000

That is, the total sales over time will be 75,000

Thus, the number for the stable sale is 75,000.