Exponential Functions Test Review

Growth or Decay

100

y=(1/3)^x

What is DECAY since b=1/3<1?

200

y= -2^{x + 1}

What is GROWTH since b=2>1 ?

300

y= -5(2/3)^x - 4

What is DECAY since b=2/3<1?

400

y= (1/2)(5)^{x - 3} +10

What is GROWTH since b=5>1?

Graphing Exponential Functions

100

What is an asymptote and how do you use it to graph?

What is an "imaginary line" on a graph that the graph of a function follows along that you draw on a graph with a dotted line?

200

What is the asymptote of the function y=2^x-3+4?

What is y=4?

300

What is the table you use to graph the function y=(1/3)(2)^x+1?

What is 

x |  0   |  1   |  2   

y | 1/3 | 2/3 | 4/3

?

400

What table would you use to graph y=3(2/3)^x+1- 7?

What is

x | -1  |  0  |  1  |  2

y |9/2 |  3  |  2  | 4/3

?

Solving Exponential Equations

100

Solve 5^x-6=125

What is x=9 ?

200

Solve 81^a+2=3^3a+1

What is a=-7 ?

300

Solve 8^2y+4=16^y+1

What is y=-4 ?

400

Solve (1/2)^4x+1=8^2x+1

What is x=-2/5 ?

Solving Exponential Inequalities

100

Solve 10^5b+2>1000

What is b>1/5 ?

200

Solve (1/64)^x-2<32^2x

What is x>3/4 ?

300

Solve 81^x+4>(1/27)^2x-2

What is x>-1 ?

400

Solve (1/36)^w+2<(1/216)^4w

What is w<2/5 ?

Word Problems

100

You deposit $1,000 in an account that earns 2.5% annual interest. Find the balance after 3 years if this interest is compounded daily.

What is $1,077.88 ?

200

You take out a student loan for $22,000 with a 7.45% interest rate compounded weekly. After you graduate college which is 4 years later, you look at the loan balance. How much do you owe with interest?

What is $29,631.24 ?

300

A population of rabbits is growing at an exponential rate. Initially there are 5,000 rabbits. After 3 years, there are 27,000 rabbits. Write the exponential function that models this situation.

What is y=5,000(1.754)^x ?

400

The population of sea turtles is decreasing exponentially. After 4 years, there are 7,000 sea turtles. After 6 years, there are 3,500 sea turtles. How many sea turtles were there initially?

What is 28,025 sea turtles ?