Exponential Functions
What is the general form of an exponential function?
f(x) = a bx
What is the formula for exponential decay?
A = P (1 - r)t
Is the following sequence arithmetic, geometric, or neither?
1, 3, 6, 10...
Neither
In what direction is the graph of y = 2x shifted to match y = 2x + h, when h > 0?
What is x * x2?
x3
What's the name of the line that a function gets closer and closer to but never crosses?
Asymptote
Aren deposited $2000 into the bank, giving an 8% interest rate per year. Write an equation to represent the situation.
A = 2000 (1.08)t
Write the recursive formula for the geometric sequence 1, 3, 9, 27, 81...
a1 = 1; an = 3 * an-1
Describe the transformation from f(x) = (1/2)x to g(x) = (1/2)x-3
Shift right 3
Simplify the equation on the board. Write as a fraction if necessary.
w2
What is the domain and range of the following equation: y = -3 (4)x ?
D: All real numbers
R: y < 0
Morgan bought a car for $10,000, and it depreciates in value at a rate of 6% per year. How much will their car be worth after 5 years? Round to the nearest dollar.
$7339
Write the explicit formula for the function based on the following recursive formula:
a1 = 7; an = (1/3) an-1
an = 7 * (1/3)n-1
What is the domain and range of the following equation: y = (1/3)x + 7?
D: All Real Numbers
R: y > 7
Simplify (2x3 )2
4x6
What is the formula for an exponential function that fits the following set of points: (0, 1/2), (1, 2), (2, 8), (3, 32)?
y = (1/2) * 4x
Gustav put $5000 into the bank under a plan where it will gain 9% interest compounded semi-annually. How much money will he have after 10 years?
$12058.57
Find the 12th term of the sequence (7/3), 7, 21, 63...
a12 = 413343
f(x) = 3x-2 + 1
g(x) = 3x-2 - 9
Describe the transformation from f(x) to g(x).
Shift 10 units down
Simplify the equation on the board. Write as a fraction if necessary.
2y2
4 rats have found their way into my basement, and if unchecked they will double every year. If nothing is done about the rats, estimate how many years it will take for there to be 5000 rats in my basement.
Between 10-11 years
Myrtle was given a fancy $5 spoon as a gift in 1920. Since vintage items tend to be given more worth when they are older, its worth grew at a rate of 36% every decade. How much would the spoon be worth in the year 2020?
$108.23
If a1 = 48 and a5 = 3 are the 1st and 5th terms in a geometric sequence, what are the first 5 terms in the sequence?
48, 24, 12, 6, 3
If f(x) = 2x, and g(x) is the result of shifting f(x) left 4 units, evaluate g(1).
g(1) = 32
If x1/2 * x1/2 = 9, what is x1/2 equal to?
x1/2 = 3