Exponential Functions Bellringer

Many times a tweet will be tweeted and then retweeted with the possible number of retweets growing exponentially. Manuel modeled this phenomenon with the function f(x) = 3(2)^x, using x to represent the number of intervals in which the tweet was retweeted. Which statement about Manuel’s function is true?

• There were 2 original tweets.
• There are 3 times 2 or 6 retweets at each level.
• At each interval, the number of retweets doubles.
• A tweet can be retweeted a maximum of 3 times.

California’s growth rate in 2013 was 0.9%. There were roughly 38 million people living in California that year. Assuming the growth rate is stable, which equation models the population P, in millions, t years after 2013?

• P = 38(1.009)^t
• P = 38(1.09)^t
• P = 38(1.9)^t
• P = 38(0.9)^t

After a dose of an antibiotic, the number of bacteria decreases. If the equation y = 27000(⅓)^x models this “decay” situation, which value represents the original number of bacteria?

• 3000
• 9000
• 27000
• 81000

Ice bucket challenges for various causes have become quite common on social media. Participants challenge others to dump a bucket of ice water over their head or make a donation. The number of people participating in a challenge is an example of exponential growth and might be modeled by a function such as f(x) = 2(2.5)^x . What does the 2.5 in this function represent?

• the average number of people each person challenged
• the average number of people who started the challenge
• the average number of gallons used in each person’s challenge
• the average number of times each person participated in the challenge

Ten members of an exercise group heard a rumor about their gym. These 10 members spread that rumor so that 42 additional members learned of it. These 42 spread the rumor further, so that about 150 additional members learned of it. Then at the next level 650 learned and finally 2560 learned of the rumor. Which equation is a reasonable fit to this data?

• y = (10 × 4)^x
• y = 10(4)^x
• y = 2.5(4)^x
• y = 4(2.5)^x

The number of maps remaining at an information booth can be modeled by the function, f(x) = 274 - 32x, where x is the number of hours that have elapsed since the booth opened. Which statement is true?

• Every hour, 274 maps are given away. 
• Every hour, 242 maps are given away.
• There were 32 maps at the booth before it opened.
• There were 274 maps at the booth before it opened

A new model of a cell phone was released while the original model was still being sold. The average number of the original model sold each week was 2750, which decreased by 21% each week after the new model was released. Which function can be used to determine the average number of original model cell phones sold each week x weeks after the new model was released?

• y = 2750 (.21)^x
• y = 2750 (.79)^x
• y = 2750 (1.21)^x
• y = 2750 (1.79)^x

The number of bacteria in a Petri dish increases by 18% every hour. If there were initially 200 bacteria placed in the Petri dish, which function can be used to determine the number of bacteria in the Petri dish in exactly x hours?

• y = 200 (0.18)^x
• y = 200 (0.82)^x
• y = 200 (1.18)^x
• y= 200 (1.82)^x

The population of a small town can be modeled by the equation
 f(t) = 4800 (1.02)^t 
where t is the number of years since the collection of the population data began. 
Which statement is true?

• The population grows at a rate of 102% each year. 
• The population will reach a maximum of 4800 people. 
• The population was 4800 when the collection of data began. 
• The population grew by 102 people each year since the collection of data began. 

The number of kilograms, y, of a radioactive element that remains after t hours can be modeled by the equation, y = 0.23(0.91)^t What is the rate of decrease of this radioactive element?

• 9%
• 23%
• 77%
• 91%