SWITCHING VARIABLES IN EQUATIONS and PLOTS Suppose you have a function shown below, where V (cm) and t (min): V = 2t What are the units of 2 and 3? How would you plot this to make it linear? What would be the slope and intercept? Suppose the equation represents the volume of a balloon V (cm) as you blow it up over time (min). Some data are below: t (min) T (sec) V (cm) 1 60 2 2 120 16 3 180 54 If you wanted to get an expression in terms of seconds instead of minutes, the temptation would be to do the following: V = 2 (t ) Why is this NOT correct? Instead, define a new variable T (sec), instead of t (min). These are related by T = t * 60 (sec/min). If we plug this into the original equation, we get: Another option is to convert the units of the coefficients, e.g. convert all "minutes" in all the coefficients into "seconds".

SWITCHING VARIABLES IN EQUATIONS and PLOTS Suppose you have a function shown below, where V(cm3) and t(min):V=2t3 What are the units of 2 and 3 ? How would you plot this to make it linear? What would be the slope and intercept? Suppose the equation represents the volume of a balloon V(cm3) as you blow it up over time (min). Some data are below: If you wanted to get an expression in terms of seconds instead of minutes, the temptation would be to do the following: V=2(t)3WhyisthisNOTcorrect? Instead, define a new variable T(sec), instead of t(min). These are related by T=t60(sec/min). If we plug this into the original equation, we get: Another option is to convert the units of the coefficients, e.g. convert all "minutes" in all the coefficients into "seconds