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

The dollar value vt of a certain car model that is t years old is given by the following exponential function.=vt20,0000.90tFind the initial value of the car and the value after 13 years.Round your answers to the nearest dollar as necessary.Initialvalue: $Valueafter13years: $

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: Interpret the function given in the context of the real-world situation described to answer the question.The projected value of an investment is modeled by the exponential function V(t)=25,000(1.115)t𝑉(𝑡)=25,000(1.115)𝑡, where V(t)𝑉(𝑡) is the total value after t𝑡 years. What is the percent increase each year for the investment?Answer 1 Question 14 %

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

As a car ages, its value decreases. The value of a particular car with an original purchase price of $27,000 is modeled by the following function, where 𝑐 is the value at time 𝑡, in years.𝑐⁡(𝑡)=27,000⁢(1-0.21)𝑡What is the value of the car when it is 4 years old?The value of the car after 4 years is $What is the total depreciation amount after 5 years?After 5 years, the total depreciation amount is $