Question

e. determine if the value for s(t) = 0 is reasonable for the context of the func s(t) = 3.4t + 8.62. explain why or why not. reasonable?
no
yes

Explanation:

Step1: Set \( S(t) = 0 \)

We start with the function \( S(t)=3.4t + 8.62 \) and set it equal to 0: \( 0 = 3.4t+8.62 \).

Step2: Solve for \( t \)

Subtract 8.62 from both sides: \( - 8.62=3.4t \). Then divide both sides by 3.4: \( t=\frac{-8.62}{3.4}\approx - 2.535 \).

Step3: Analyze the context

In most real - world contexts (like time, quantity, etc. that \( t \) might represent), a negative value of \( t \) (such as \( t\approx - 2.54 \)) may not make sense. For example, if \( t \) represents time (in minutes, hours, etc.), negative time is not a valid concept in the context of most real - life situations related to the function \( S(t) \). So, the value \( S(t) = 0 \) is not reasonable because it leads to a negative value of \( t \) which is likely to be outside the domain of valid inputs for the context of the function.

Answer:

No (and the explanation is as above that solving \( S(t) = 0 \) gives a negative \( t \) which is often invalid in real - world contexts related to the function).