Exponential Equations
Growth & Decay
Geometric Sequences
Graphing Exponentials
AROC
100
What do "a" and "b" represent in the exponential equation
y=a*b^x
a = initial amount
b = rate
100
Which represents growth, and which represents decay?
(1+%)
(1-%)
(1+%) represents growth
(1-%) represents decay
100
Write the explicit formula for a geometric sequence:
an =
an = a1 (r)n-1
100
Describe the line of an exponential graph
It is a curved line.
100
What does AROC stand for?
Average Rate Of Change
200
If a = 14, b = 1/3, and x = 7, write the exponential equation.
y=14(1/3)^7
200
Which functions represent growth?
a) y=9(1.03)^x
b) y=4(0.97)^x
c) y=5(3.5)^x
d) y=7(1/2)^x
A and C are growth functions
200
Find the common ratio for these two sequence:
a) 7, -14, 28, -54...
b) 500, 100, 20, 4...
a) r = -2
b) r = 1/5
200
How does the graph of exponential decay look different than exponential growth?
Growth increases and goes up, decay decreases and goes down.
200
What are the 2 steps to find the AROC
Step 1: Find two points
"Step 2: " (Deltay)/(Deltax)
300
An iPad's value depreciates by half every year. The value of the iPad in 5 years is $60. Write the exponential equation that can help you find the initial amount of the iPad.
60=a(1/2)^5
300
A population of 400 ants is growing by 15% every day. Write an equation that can be used to find the population in 6 days.
y=400(1.15)^6
300
Using the following geometric formula, find the 8th term in the sequence:
an = 2(5)n-1
a8 = 156,250
300
The graph of the following function decreases and will forever and ever get closer and closer to what number?
y=10(1/2)^x-3
Get closer and closer to -3
300
Find the AROC from x=3 to x=5
AROC = 3
400
Zombies have taken over REV. There were only 4 zombies to start, but they have doubled in size every day since then. How many zombie wildcats are there in 2 weeks?
65,536 zombie wildcats
400
What percentage growth or decay is the following equation representing?
y=3(0.81)^x
19% decay
400
Write the explicit formula for the following sequence:
-3, -12, -48, -384...
an = -3(4)n-1
400
Is the following graph linear or exponential?
Neither!
400
Find the AROC from x= -4 to x=5 (answer as a fraction)
AROC = 10/9
500
Here's an exponential table. Write the exponential equation:
y=5*3^x
500
A car depreciates by 8% every year. If the car costed $17,000 when it was first purchased, how much does the car cost in 7 years? Round to the nearest cent.
$9,483.39
500
Which sequence is geometric? Which is arithmetic? Why?
a) 4, 8, 12, 16, 20...
b) 4, 8, 16, 32, 64...
A is arithmetic because it is adding by 4.
B is geometric because it is multiplying by 2.
500
Complete the table for the function y=2(-4)x
500
Find the AROC of the following function over the interval [0,6]
y=4(2)^x
AROC = 42