Distinguishing Exponential & Linear from Context EOC Review: Distinguishing Exponential & Linear from Context

Exponential or Linear? Sometimes we need to identify whether a table is displaying data that follows an exponential or a linear pattern. Look for key words & patterns.

KEY TERMS EXPONENTIAL LINEAR GROWTH/DECAY CONSTANT PERCENT RATE OF CHANGE DOUBLES/HALVES EACH, EVERY, RATE, PER CONSTANT RATE OF CHANGE SLOPE

TABLE PATTERNS EXPONENTIAL LINEAR LOOK FOR A CONSTANT MULTIPLYING PATTERN (*sometimes will look like dividing because it is multiplying by a fraction) LOOK FOR A CONSTANT ADDING PATTERN (*sometimes will look like subtracting because it is adding a negative)

Example: E#1.1 Check the pattern in the table. x y 4 2 14 3 19 5 29 Which type of function best models the data shown in the table? A. a linear function, because y is changing at a constant rate per unit interval of x B. a linear function, because y is changing at a constant percent rate per unit interval of x C. an exponential function, because y is changing at a constant rate per unit interval of x D. an exponential function, because y is changing at a constant percent rate per unit interval of x x y 4 2 14 3 19 5 29 Eliminate contradictory answers: B. Linear ≠ constant PERCENT rate C. Exponential ≠ constant rate

Example E#1.2 Three students in a class collected results from three labs numbers. The table below shows the results each student collected. Which student collected data that would best be modeled by an exponential function? A. Olivia B. Maleek C. Tyasia D. None of them Notice the question is looking for exponential… so look for a multiplying pattern.   Lab 1 Lab 2 Lab 3 Olivia 120 240 480 Maleek 90 150 Tyasia 200 210

You Try! Mark key terms. Look for patterns in the table.

Check it E#1.3 Which type of function best fits the data in the table below? A. exponential decay model B. exponential growth model C. linear model with positive slope D. linear model with negative slope x y -2 80 -1 20 5 1 1.25

Check it: E#1.4 Which type of function best fits the data in the table below? A. exponential decay model B. exponential growth model C. linear model with positive slope D. linear model with negative slope x y 0.15 1 0.6 2 2.4 3 9.6

Check it: E#1.5 Four students in a class charted the results of four races. The table below shows the data each student charted. Which student charted data that would best be modeled by a linear function? A. Jojo B. Nono C. Niko D. None of them Race 1 Race 2 Race 3 Race 4 Jojo 120 sec. 110 sec. 100 sec. 90 sec. Nono 180 sec. 200 sec. Niko 240 sec. 60 sec. 30 sec.