Question

With your computer now loaded, you bring up the data for your experiment. The data suggests that your experiment can be modeled by a linear equation. Specifically, the volume as a function of time is v(t)=3 10t. 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?

Answer 1

To find the inverse relationship of the linear equation v(t) = 3×10t, representing volume as a function of time, we swap the variables and solve for time to obtain the inverse function t(v) = v/(3×10).

Step-by-step explanation:

The student's data suggests that the experiment can be modeled by a linear equation, specifically the volume as a function of time, given by v(t) = 3×10t. To find the inverse relationship, we want to express time as a function of volume, which will allow us to calculate the time it takes to reach a given volume. The steps to find the inverse function are as follows:

1. Write the equation in 'y = ...' form: y = 3×10t.
2. Swap the variables: t = 3×10y.
3. Solve for y: y = t/(3×10).

Therefore, the inverse function is t(v) = v/(3×10), which shows the amount of time 't' it takes to achieve a given volume 'v'.