Which of the contexts below could be modeled by an exponential function?AnswerMultiple Choice AnswersA music service has a fixed monthly cost and charges $0.40 for each downloaded song.A sunflower was growing at a rate of 1 inches per week.A radioactive compound decays at a rate of 13% per hour.Snow was melting at a rate of 2.5 inches per hour.

Which of the contexts below could not be modeled by an exponential function?AnswerAttempt 1 out of 2Multiple Choice AnswersA coin collection appreciates at a rate of 17.2% per year.A music service has a fixed monthly cost and charges $0.20 for each downloaded song.A car depreciates at a rate of 2.7% per year.Money invested in a savings account grows at an annual rate of 3.4%.

Which of the contexts below could be modeled by an exponential function?AnswerAttempt 1 out of 2Multiple Choice AnswersAn elevator descends at a rate of 17 feet per second.An amusement park charges $2.50 to go on each of the rides.A taxi charges a flat fee of $3.50 for pick-up, then an additional fee of $4.75 per mile.A coin collection appreciates at a rate of 8% per year.

Which of the contexts below could not be modeled by an exponential function?AnswerMultiple Choice AnswersA town's population shrinks at a rate of 8.1% every year.A certain population of 41 aggressive zombies doubles every week.Snow was melting at a rate of 2.5 inches per hour.A radioactive compound decays at a rate of 29% per hour.

Which of the contexts below represents exponential growth?AnswerAttempt 1 out of 2Multiple Choice AnswersA music service has a fixed monthly cost and charges $0.65 for each downloaded song.A town's population grows at a rate of 7.2% every year.The amount of a certain medication in a person's bloodstream decreases by start fraction, 3, divided by, 5, end fraction 53​ every week.A radioactive compound decays at a rate of 26% per hour.

Let’s do an example together that is an exponential decay model.ProblemThe cost of a new car is $32,000$32,000. It depreciates at a rate of 15%15% per year. This means that it loses 15%15% of its value each year.Draw a graph of the car’s value against time in years.Find the formula that gives the value of the car in terms of time.Find the value of the car when it is four years old. SolutionThis is an exponential decay function. Start by making a table of values. To fill in the values we start with when t=0𝑡=0. Then we multiply the value of the car by 85%85% for each passing year. (Since the car loses 15%15% of its value, it keeps 85%85% of its value. 100−15=85100−15=85.) Remember 85%=0.8585%=0.85.Time Value (Thousands)0032321127.227.22223.123.13319.719.74416.716.75514.214.2The general formula is y=a(b)x𝑦=𝑎(𝑏)𝑥. In this case y𝑦 is the value of the car, x𝑥 is the time in years, a=32,000𝑎=32,000 is the starting amount in thousands, and b=0.85𝑏=0.85 since we multiply the value in any year by this factor to get the value of the car in the following year. The formula for this problem is:y=𝑦= (( )x)𝑥Finally, to find the value of the car when it is four years old, we use x=4𝑥=4 in the formula. Remember the value is in thousands.y=32000(0.85)4=𝑦=32000(0.85)4= At 44 years old, we expect the car to be worth $$ CheckQuestion 2