Geometric Sequences to Exponential Functions

Convert to an exponential function in standard form:
 $g_n=4\left(2\right)^{\left(n-1\right)}$  

•  $f\left(x\right)=8\left(2\right)^x$  

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

•  $f\left(x\right)=8\left(2\right)^{\left(x-1\right)}$  

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

Convert to an exponential function in standard form:
 $g_n=5\left(\frac{1}{2}\right)^{\left(n-1\right)}$  

•  $f\left(x\right)=2.5\left(\frac{1}{2}\right)^x$  

•  $f\left(x\right)=5\left(2\right)^x$  

•  $f\left(x\right)=10\left(\frac{1}{2}\right)^x$  

•  $f\left(x\right)=5\left(10\right)^x$  

What is the first term of this geometric sequence?
 $g_n=100\left(\frac{1}{2}\right)^{\left(n-1\right)}$  

•  $\frac{1}{2}$  

• 200

• 100

• 50

If this geometric sequence is converted to standard form of an exponential function, what is the y-intercept?
 $g_n=9\left(\frac{1}{3}\right)^{\left(n-1\right)}$  

• 27

• 9

• 3

•  $\frac{1}{3}$  

What is the growth factor of the function below?
 $h\left(x\right)=4\left(1.25\right)^x$  

• 4

• 5

• 3.2

• 1.25

Which of the following can be said about the function below?
 $f\left(x\right)=4\left(\frac{3}{4}\right)^x$  

• The function is linear

• The function is increasing

• The function is decreasing

• The function is quadratic

Which of the following can be said about the function below?
 $f\left(x\right)=3x-7$  

• The function is linear

• The function is exponential

• The function is decreasing

• The function is quadratic

Which of the following can be said about the function below?
 $f\left(x\right)=\frac{1}{2}\left(3\right)^x$  

• The function is linear

• The function is exponential

• The function is decreasing

• The function is quadratic

Which of the following defines the geometric sequence shown in the table?

• $g_n=72\left(0.8\right)^{\left(n-1\right)}$

• $g_n=72\left(1.25\right)^n$

• $g_n=72\left(1.25\right)^{\left(n-1\right)}$

• $g_n=72\left(0.8\right)^n$

Which of the following exponential functions contains all of the points shown in the table above?

•  $f\left(x\right)=72\left(1.25\right)^x$ 

•  $f\left(x\right)=72\left(0.8\right)^x$ 

•  $f\left(x\right)=57.6\left(1.25\right)^x$ 

•  $f\left(x\right)=90\left(0.8\right)^8$