Exponential Functions and Geometric Sequences

In an exponential function y = ab^x, what does the 'a' represent? 

• slope
• rate of change
• y-intercept
• common ratio

What type of function is f(x)=2(1/7)^x ?

• Exponential Growth

• Linear

• Exponential Decay

• Quadratic

Which equation matches the graph?

• y=2(2)^x
• y=2(1/2)^x
• y=2^x
• y=1/2(2)^x

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

• y=6(0.14)^x
• y=6(1+14)^x
• y=6(1.14)^x
• y=6(0.86)^x

Find the 22nd term of the following sequence:
5, 8, 11, ...

• 14
• 68
• 63
• 71

Create the explicit formula for the sequence:
2, 8, 14, ...
(Hint:  Write your formula and then simplify it.)

• a_n=2+6n
• a_n=-6+6n
• a_n=6n-4
• a_n=4-6n

Find the common ratio: 4, -16, 64, -256, ...

• r = -4
• r = 2
• r = -2
• r = 4

In a sequence, the first term is 8 and the common difference is 6. The fifth term of this sequence is

• -22

• -16

• 32

• 38

Select the TRUE statements about the functions

 $f\left(x\right)\ =\ 2x-4$  
 $g\left(x\right)\ =\ 2^x\ -\ 4$  
 $h\left(x\right)=\left(\frac{1}{2}\right)^x\ -\ 4$  
 $k\left(x\right)\ =\ \frac{1}{2}x-4$  

•  $f\left(x\right)$  and  $k\left(x\right)$  are linear.

•  $g\left(x\right)$  is exponential growth. 

•  $h\left(x\right)$  is exponential decay.

•  $f\left(x\right)\ and\ g\left(x\right)$  are both exponential growth. 

•  $h\left(x\right)\ and\ k\left(x\right)$  are both exponential decay.

Suppose you deposit $1000 in a college fund that pays 7.2% interest compounded annually. Find the account balance after 5 years.