From 1990 to 1994, the mail order sales of health products in the United States can be modeled by

S = 10t^3 + 115t^2 + 25t + 2505

where S is the sales (in millions of dollars) and t is the number of years since 1990. In what year where about $3885 million of health products sold?

Just plug in 3885 for S in the equation and solve.

How would I find out the year by plug in 3885 for S and solving?

You have only one variable (t) to solve for.

Isolate the variable on one side of the equation and solve for it.
For this problem you will have to subtract 2505 from bother sides of the equation.
Then factor the remaining equation of t.

To find the year when about $3885 million of health products were sold, we need to solve the equation S = 3885, where S is the sales.

Using the given equation S = 10t^3 + 115t^2 + 25t + 2505, we substitute 3885 for S:
3885 = 10t^3 + 115t^2 + 25t + 2505

Now, we need to solve this equation to find the value of t (the number of years since 1990) when the sales were approximately $3885 million.

To solve a cubic equation like this, we can use either numerical methods or algebraic methods such as factoring or synthetic division. In this case, we will use numerical methods to find an approximate solution.

We can use a graphing calculator or software to plot the function f(t) = 10t^3 + 115t^2 + 25t + 2505 and find the approximate value of t that corresponds to f(t) = 3885.

By entering the equation into a graphing calculator or software and graphing it, you can find the intersection point of the graph with the horizontal line at y = 3885. This intersection point will give us the approximate value of t.

Note: Depending on the graphing calculator or software you are using, the steps may vary slightly. Here is a general process:

1. Enter the equation into the graphing calculator or software.
2. Set the calculator or software to the appropriate range for t (e.g., from 0 to 4) to cover the period from 1990 to 1994.
3. Graph the equation.
4. Find the intersection point of the graph with the horizontal line y = 3885.
5. Read the x-coordinate (t-value) of the intersection point, which corresponds to the year.

Using this method, you should find that the approximate year when about $3885 million of health products were sold is around 1992.