Exponents and Desmos

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. The equation is given by y=4000(1.25)^x .How many mosquitoes will there be after 4 months?

• 9779

• 9006

• 9765

• 5433

What is the domain of y=2(1.5)^X?

Hint: Type the equation in DESMOS to see the graph

• y is less than 0

• x is less than 12

• y greater than 0

• All Real Numbers

Which of the following functions is represented by this graph?

Hint: DESMOS

• f(x)=2(1.2)^x

• f(x)=2(0.75)^x

• f(x)=6(0.75)^x

• f(x)= −2(0.75)^x

Elise has $100 in her bank account. The account earns 2% interest every year. y=100(1.025)^x represents the amounts, y, in dollars, of the bank account after, x years. Which statement is the best interpretation of one of the values in this function?

• The initial amount is $1.02

• The amount increases by a rate of 2%

• The amount decreases by a rate of 1.025%

• The amount at the end of one year is $100

The value of a car is $15,000 and depreciates at a rate of 8% per year. The exponential function is given by: a(x)= 15000(0.92)^x. What does 15000 represent?

• The growth factor

• The decay factor

• The original value of the car

• The value of the car in Year 10

Which statement about the graph y=4(0.667)^X is FALSE?

Hint: Type in DESMOS to see the grapg

• The graph has a horizontal asymptote

• The graph has an asymptote at y=0

• The graph decreases from left to right

• The graph touches the y-axis at (0,5).

What is the range of the function?

• y > 0

• y < 2

• x>2

• x<1

What is the y-intercept of the function?

• 2
• 3
• 1
• -2

A new savings account is opened with $400 and gains 3% every yr. What is the exponential equation?

• f(x)= 400(.03)^x
• f(x)= 400(1.03)^x
• f(x)= 400(3)^x
• f(x)= 400(.97)^x

The NCAA basketball tournament starts with 64 teams.  During each round, half of the teams are eliminated.  What is the y-intercept for this function?

• (64, 0)
• (0, 0)
• (0, 64)
• Cannot be determined