Exponential Functions

The value of a piece of equipment is decreasing at a rate of 7.5% yearly. If the equipment was valued at $930 when it was purchased, which of the following represents the value of the equipment, x years after it was purchased?

• f(x) = 930(0.925)^x
• f(x) = 930 - 7.5x
• f(x) = 9300(0.075)x
• f(x) = 0.925x - 930

Mrs. Sanchez is conducting an experiment. The number of bacteria in a sample quadruples every 24 hours. There were 35 bacteria in the initial sample. Which of the following functions shows the number of bacteria, f(x), in the sample after x days of the experiment?

• f(x) = 35(24)^x
• f(x) = 35(4)^x
• f(x) = 24(4)^x
• f(x) = 24(35)^x

The table contains some points on the graph of an exponential function. Based on the table, which function represents the same relationship?

• f(x) = (125)^x
• f(x) = (2.4)^x
• f(x) = 0.75(2.4)^x
• f(x) = 0.125(2.4)^x

The function y = 2x is shown above. If the function translated up 4 units, which of the following would represent the y- intercept and the equation of the horizontal asymptote of the translated function?

• (0, 5); y = 4
• (5, 0); y = 4
• (0, 5); x = 4
• (5, 0); x = 4

The function f(x) = (0.5)(2)^x is shown on the graph. What is the y-intercept of the function?

• 2
• -5
• 0.5
• -6

An exponential function is shown. What is the horizontal asymptote of this function?

• x = 0
• y = -2
• x = 2
• y = 0

Which answer choice best represents the sequence below:  $4,\ 8,\ 16,\ 32,\ 64,\ 128,\ 256,...$  

•  $f\left(x\right)=2\left(4\right)^x$  

•  $f\left(x\right)=4\left(2\right)^x$  

•  $f\left(x\right)=4\left(2\right)^{x-1}$  

•  $f\left(x\right)=4+2\left(n-1\right)$  

When a ball bounces, the heights of consecutive bounces form a geometric sequence. The height of the first bounce is 121 centimeters and the height of the third bounce is 64 centimeters. To the nearest centimeter, what is the height of the fifth bounce?

• 25

• 36

• 38

• 42

Marilyn collects old dolls. she purchases a doll for $450. Research shows this dol's value will increase by 2.5% each year. Write an equation that determines the value, V, of the doll t years after purchase.

• $V\left(t\right)=450\left(1+0.025\right)^t$

• $V\left(t\right)=450\left(1-0.025\right)^t$

• $V\left(t\right)=450\left(1+2.5\right)^t$

• $V\left(t\right)=450\left(1-2.5\right)^t$

A student invests $500 for x years in a savings account that earns 4% interest per year. Write a function that represents the amount of money in the account after x years.

• $f\left(x\right)=500\left(.60\right)^x$

• $f\left(x\right)=500\left(.96\right)^x$

• $f\left(x\right)=500\left(1.04\right)^x$

• $f\left(x\right)=500\left(1.4\right)^x$