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

Prakash bought a new car at the dealership for $27,000. It is estimated that the value of the car will decrease 7% each year. Which exponential function models the value v of the car after t years?A.𝑣=27,000(0.93)𝑡v=27,000(0.93) t B.𝑣=27,000(1.3)𝑡v=27,000(1.3) t C.𝑣=27,000(1.03)𝑡v=27,000(1.03) t D.𝑣=27,000(0.3)𝑡v=27,000(0.3) t SUBMITarrow_backPREVIOUS

Which of the contexts below could not be modeled by an exponential function?AnswerMultiple Choice AnswersA car depreciates at a rate of 3.7% per year.A sunflower was growing at a rate of 2.75 inches per week.A certain population of 25 aggressive zombies quadruples every week.Money invested in a savings account grows at an annual rate of 2.2%.

Instructions: Graph the following function. Then, state whether the function represents exponential growth or decay.y=(45)x𝑦=(45)𝑥This function is exponential

We have to deal with problem-solving in many real-world situations. Therefore, it is important to know the steps you must take when problem-solving depending on the type of problem. Let's use exponential functions to solve the following problems:Suppose $4000$4000 is invested at a 6%6% interest rate compounded annually. How much money will there be in the bank at the end of five years? At the end of 2020 years?Read the problem and summarize the information.$$ is invested at a %% interest rate compounded annually. We want to know how much money we will have after and after years.Assign variables.x=𝑥= time in yearsy=𝑦= amount of money in the investment account.We start with $4000$4000 and each year we apply a 6%6% interest rate on the amount in the bank. The pattern is that each year we multiply the previous amount by a factor of 100%+6%=106%=1.06100%+6%=106%=1.06. Complete a table of values by continuing to multiply each year’s amount by 1.061.06.

Which of the contexts below represents exponential decline or decay?AnswerAttempt 1 out of 2Multiple Choice AnswersAn elevator descends at a rate of 24 feet per second.Money invested in a savings account grows at an annual rate of 2.2%.A car depreciates at a rate of 7.3% per year.A population of 150 bacteria doubles every minute.