Translations
Adding or subtracting a number from x in an exponential function shifts the graph ______.
Left or right
Without using a calculator!
Is the function below showing growth or decay?Explain your answer.
f(x)=0.5(1.8)^x
growth, the common ratio, b, is greater than 1
What is an exponential function's multiplier if something is being tripled?
3
Exponential functions are growth functions when which variable is greater than 1?
hint: recall the equation y=a(b)^x
b (The common ratio)
The answer to the equation when x is 6
y = 2^x
What is 64?
Adding or subtracting a number from the end of the function shifts the graph ______.
up or down
Which number illustrates that this exponential function is decaying?
y = 20 xx 0.5^x
0.5
What is an exponential function's multiplier if something is being doubled?
2
consider the function below. What is the percent increase?
f(x)=200(1.05)^x
5%
What is the balance of a $4,000 principal earning 6% interest compounded annually, after 5 years.
$5352.90
Which number in the function below represents a horizontal shift to the right.
y = (1/2)^(x-1) + 2
-1
These two terms are used in practical application and modeling exponential problems to represent increasing and decreasing functions.
growth and decay
The number of times interest is compounded if it is done quarterly?
4
What is the variable in an exponential function that represents the initial value of whatever is being measured for modeling problems.
hint: recall the equation a(b)^x
a
An investment of $5000 doubles in value every decade. What is the amount in the account after 30 years.
$40,000
What is the direction and number of steps the following function shifts vertically:
3^(x-3)-2
down 2
Exponential functions are decay functions when the variable b is between what two numbers.
0 and 1
To convert a growth or decay factor from years to days, you would divide it by this number.
365
The variable b in an exponential function can be called_______.
hint: recall y=a(b)^x
Base, common ratio, multiplier, Growth/Decay factor
What is the function that models the number of 800 amoeba in a petri dish that doubles in size every 20 minutes, where x is the number of 20 minute periods.
800 xx 2^x
What is the number and direction of the horizontal shift in the function
y = 2 xx (1/2)^(x + 2) + 1
left 2 units
What is the population of a city of 45,000 people with a decreasing rate of 2% per year after 15 years.
33,236 people
To convert a growth or decay factor from months to years, you would divide it by this number.
12
Consider the function below? What is the percent decrease?
f(x)=150(0.98)^x
2%
The statement among these four that is not true regarding the function
y = 2^x
A. The function is an exponential function.
B. The function has a domain of all real numbers.
C. As the value of x gets very large, the value of y gets close to zero.
D. As the value of x increases by one, the value of y doubles.
C As the value of x gets very large, the value of y gets close to zero.