An olympic swimmer is having his laps timed during practice. To be aware of his progress, the results are shown as order pairs (l, t) below: (1,19), (2,38), (3,57) (4,76). Which equation represents t, the time in seconds, as a function of l the number of laps that the swimmer has finished?
A: t(l) = l + 19
B: l(t) = t/19
C: l(t) = 19t
D: t(l) = 19l
Is it "C"
"represents t, the time in seconds, as a function of l the number of laps"
means that l is the independent variable, and t(time) is the dependent variable. Therefore you only have a choice between A and D. Choose the one with the correct relation.
Yes, you are correct. Equation C, l(t) = 19t, represents the time in seconds (t) as a function of the number of laps (l) that the swimmer has finished.
To determine the equation that represents time (t) as a function of the number of laps (l), we need to observe the given ordered pairs and look for a pattern.
By examining the given pairs, we can see that for each additional lap, the time increases by 19 seconds. This means that for every increase of 1 in the number of laps, the time increases by 19 seconds.
Therefore, the correct equation would show that t is directly proportional to l, with a constant rate of increase of 19 seconds per lap.
Looking at the given options:
A: t(l) = l + 19
B: l(t) = t/19
C: l(t) = 19t
D: t(l) = 19l
Among these options, the equation that adequately represents the relationship between time (t) and the number of laps (l) is option D: t(l) = 19l. This equation signifies that for each lap completed, the time increases by 19 seconds.
Hence, the correct answer is D: t(l) = 19l.