Question

The number of bacteria grown in a lab can be modeled by P(t)-300 2t, where t is the number of hours. Which expression equivalent to P(t)? (1) 300 8 (2) 300 16 (3) 300 24 4) 300.22 During physical education class, Andrew recorded the exercise times in minutes and heart rates in beats per minute (bpm) of four of his classmates. Which table best represents a linear model time and heart rate of exercise Student 1 Exercise Heart (in minutes) (bpm) Student 3 Exercise Heart (in minutes) (bpm) Rate Time Rate Time 0 0 65 70 75 65 70 75 79 2 3 Student 4 ExerciseHeart (in minutes) (bpm) Student 2 ExerciseHeart Rate Time Time Rate (in minutes) (bpm) 62 70 83 0 65 2 3 4 2 3 4 73 90 75

Answer 1

1. We have P(t) = 300*2^4t = 300*(2⁴)^t = 300*16^t . The 2^nd option is the correct answer.

2. It may be observed that only in the 1^st case, for the same difference in x-values ( exercise time), the corresponding difference in the y-values ( heart rate) is constant. In all other cases, the difference in the y-values varies. Hence , only the 1^st case represents a linear relationship between the exercise time and the heart rate. For visual clarity, scatter plots of all the data sets are attached.