Problem
check your work. follows the SNHU late policy. ng "Quit \& Save". This will save all answers and explanations. fone working as this finalizes your assignment and you will lose access to make any changes. d your project and it is ready for grading. With your computer now loaded, you bring up the data for your experiment. The data suggests that your experiment can be modeled as by a linear equation. Specifically, the volume as a function of time is $V(t)=15+14 t$. You have been asked to determine the inverse relationship so that the amount of time it will take to reach a given volume can be found. What function do you provide? Enclose numerators and denominators in parentheses. For example, $(a-b) /(1+n)$. \[ t(V)= \] 중 준 Explain, in your own words and with your own work, how you arrived at this result. Be sure to
Solution
Step 1 ：The question is asking for the inverse of the function \(V(t)=15+14 t\). To find the inverse of a function, we need to switch the dependent and independent variables and solve for the new dependent variable. In this case, we need to switch \(V\) and \(t\) and solve for \(t\).
Step 2 ：The original equation is \(V = 14t + 15\).
Step 3 ：To find the inverse, we switch \(V\) and \(t\) to get \(t = V - 15/14\).
Step 4 ：Solving for \(t\), we get \(t = V/14 - 15/14\).
Step 5 ：So, the inverse function is \(\boxed{t(V) = \frac{V}{14} - \frac{15}{14}}\). This function will give the time it takes to reach a given volume.
