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
(1+r) is for growth and (1-r) is for decay.
The rate is more than 1 for growth models but less than 1 for decay models.
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
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
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
Evaluate the following exponential expression so there is a single term solution.
364/6 divided by 361/6
6
What is the domain and range of the function:
-3^(-x+2)-1
Domain: all real numbers
Range: y < -1
What is the rate of change from x= - 6 to x = for the function
y=4^x+3
(-6,3)(2,19)
rate of change = 2
Brenda invests $4,848 in a savings account with a fixed annual interest rate of 5% compounded semiannually What will the account balance be after 6 years?
$6,520.02
In 2002 the population of schoolchildren in a city was 90,000. This population decreases at a rate of 5% each year. What will be the population of school children in year 2010?
59,708 schoolchildren