Features of Exponential Functions
What is the initial value of the exponential function? (-1,1.5) (0,3) (1,6) (2,12) (3,24) (4,48)
(0,3)
Write the exponential function with a common ratio of 1/2 and an initial value of 6.
f(x)=6(1/2)x
A colony of bacteria triples every hour. The colony starts at a population of 2. Write an expression to determine the bacteria population after 7 hours.
f(x)=2(3)7
Is the following sequence arithmetic or geometric? If geometric, state the common ratio.
1/2, 1/4, 1/8, 1/16...
Geometric... common ratio of 1/2
What is the asymptote of the function f(x)=2x-7?
y = -7
Describe the transformation of the function g(x)=3x-2 from the function f(x)=3x.
Horizontal shift right 2.
Your local bank is offering a checking account with 1% interest. You decide to deposit $100 in this account. Write the exponential growth model for this situation.
f(x) = 100 (1.01)x
Rewrite the following in radical form.
51/3
cube root of 5
What is the domain and range of the following:
y=5(4)^x
Domain: all real numbers
Range: y > 0
Use the explicit formula to find the 9th term of the sequence.
2, 8, 32, 128 ...
131, 072
Meg just bought a new cell phone worth $800 but knows that her phone will lose 8% of its value every year. Write an exponential decay model for this situation.
Rewrite the following exponential in radical form:
3^(5/3)
root(3)(3^5)
What is the domain and range of the function:
(1/2)^x+3
Domain: all real numbers
Range: y > 3
Describe the transformation of the function g(x)=4-x from the function f(x)=4x.
A horizontal reflection. (Reflection over the y-axis)
Suppose you're studying a virus strain that creates 4 new viruses every hour. You start your study by injecting 5 viruses into a lab rat. After 5 hours, how many viruses will there be in the rat?
5120 viruses
Which of the following is not equivalent to (42x)3
(46)x
(43x)2
(44x)2
(42)3x(44x)2
What is the domain and range of the function:
-3^(-x+2)-1
Domain: all real numbers
Range: y < -1
Write the exponential function that...
- is vertically translated down 4
- horizontally translated left 3
- has a common ration of 4
- has an initial value of 0.25
f(x)= 0.25(4)x+3 - 4
Brenda invests $4,848 in a savings account with a fixed annual interest rate of 5% compounded annually. What will the account balance be after 6 years?
$6,496.78
Evaluate the following exponential expression so there is a single term solution.
364/6 divided by 361/6
6