Exponential Functions SAT Prep

f(x) = 5,470(0.64)^x/12

The function fgives the value, in dollars, of a certain piece of equipment after x months of use. If the value of the equipment decreases each year by p% of its value the preceding year, what is the value of p?

• 4

• 5

• 36

• 64

According to Moore's Law, the number of transistors included on microprocessors doubles every 2 years. In 1985, a microprocessor was introduced that had 275,000 transistors. Based on this information, in which of the following years does Moore's Law estimate the number of transistors to reach 1.1 million?

• 1987

• 1989

• 1991

• 1994

The table above gives the values of the function f for some values of x. Which of the following equations could define f?

• f(x) = 5(2^x+1)

• f(x) = 5(2^x)

• f(x) = 5(2^-(x+1))

• f(x) = 5(2^-x)

Bacteria are growing in a liquid growth medium. There were 300,000 cells per milliliter during an initial observation. The number of cells per milliliter doubles every 3 hours. How many cells per milliliter will there be in 15 hours after the initial observation?

• 1,500,000

• 2,400,000

• 4,500,000

• 9,600,000

The equation above models the number of members, M, of a gym t years after the gym opens. Of the following, which equation models the number of members of the gym q quarter years after the gym opens?

• M = 1,800(1.02)^q/4

• M = 1,800(1.02)^4q

• M = 1,800(1.005)^4q

• M = 1,800(1.082)^q

What is the y-intercept of the graph shown?

• (0,0)

• (0,2)

• (2,2)

• (2,0)

A scientist initially measures 12,000 bacteria in a growth medium. 4 hours later, the scientist measures 24,000 bacteria. Assuming exponential growth, the formula P = C(2)^rt gives the number of bacteria in the growth medium, where r and C are constants and P is the number of bacteria t hours after the initial measurement. What is the value of r?

• 1/12,000

• 1/4

• 4

• 12,000

A rubber ball bounces upward one-half the height that it falls each time it hits the ground. If the ball was originally dropped from a distance of 20.0 feet above the ground, what was its maximum height above the ground, in feet, between the third and fourth time it hit the ground?

Mathematical Equivalence

ON

A certain college had 3,000 students enrolled in 2015. The college predicts that after 2015, the number of students enrolled each year will be 2% less than the number of students enrolled the year before. Which of the following functions models the relationship between the number of students enrolled, f(x), and the number of years after 2015, x?

• f(x) = 0.02(3,000)^x

• f(x) = 0.98(3,000)^x

• f(x) = 3,000(0.02)^x

• f(x) = 3,000(0.98)^x

From 2005 through 2014, the number of music CDs sold in the United States declined each year by approximately 15% of the number sold the preceding year. In 2005, approximately 600 million CDs were sold in the United States. Of the following, which best models C, the number of millions of CDs sold in the United States, t years after 2005?

• C = 600(0.15)^t

• C = 600(0.85)^t

• C = 600(1.15)^t

• C = 600(1.85)^t