Constructing Exponential Functions

James has a 70 inch giant peach. It doubles in size every week. Write an expression that would represent how big the peach is after x weeks.

• y=2(70)^x

• y=70(2)^x

• y=1/2(70)^x

• y=70(1/2)^x

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

• y = 15(35)^x
• y = 15(1 +.35)^x
• y = 15(1- .35)^x
• y = 35(1.15)^x

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

• y=.08(15000)^x

• y=15,000(1.08)^x

• y=15,000(0.92)^x

• y=15,000(0.08)^x

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.70)^x

• y=30(5000)^x

• y=5000(1.30)^x

• y=5000x^x

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. Which equation represents the population of mosquitoes, y, after x, number of months.

• f(x)= 4000 (1.25)^x

• f(x)= 1.25 (4000)^x

• f(x)= 4000 (0.75)^x

• f(x)= 0.75 (4000)^x

You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. Which equations best represents the value of the land, y after x, number of years?

• y = 30000(5)^x

• y = 30000(0.95)^x

• y = 30000(0.05)^x

• y = 30000(1.05)^x

Use the function, N = 14,000(.96)^{t t}o represent the amount of money owed (N) for a loan after t, amount of years. What does 14,000 represent in this situation?

• The amount left at the end of the loan

• The starting amount of the loan

• The rate the loan is paid off

• The amount of interest the loan has received

Identify the y-intercept (initial value) in the function f(x)=13(.27)^x

• (.27)^x
• .27
• 13
• 3.51

Is the pictured graph growth, decay, or linear or none?  

• Exponential Growth
• Exponential Decay
• Linear
• None

The population of turtles on an island is at 50. Every year the population triples. Which equation best represents the situation above is P represents the population of turtles after t, amount of years?

• P = 3(50)^t

• P = 1/3(50)^t

• P = 50(3)^t

• P = 50(1/3)^t