The projected annual sales (in dollars) of a new product are given by the equation S=150,000+3000t, where t is the time in years from 2005. Such an equation is called a trend equation. Find the projected annual sales for 2010. Is S a function of t?
since S is a polynomial, it is a function.
2010 is 5 years from 2005, so t=5
A = 150000 + 3000*5 = 150000+15000 = 165000
To find the projected annual sales for 2010, we need to substitute t=5 into the equation.
S = 150,000 + 3000t
Plugging t=5 into the equation, we have:
S = 150,000 + 3000(5)
S = 150,000 + 15,000
S = 165,000
Therefore, the projected annual sales for 2010 are $165,000.
Now, to address the second part of your question, "Is S a function of t?"
Yes, S is a function of t. In the given equation, S is the output variable (the dependent variable) and t is the input variable (the independent variable). The value of S depends on the value of t. Every value of t corresponds to a unique value of S, making it a function.
In this case, the function S represents the projected annual sales based on the time in years from 2005.