Exponential Basics
A population starts at 20 birds and doubles every 10 years. Write an exponential function that models this growth.
What is P(t) = 20(2)^(t/10)?
The range of (x) = 2x − 4 on 2 ≤ x ≤ 6.
What is 0 ≤ y ≤ 8?
This is an explicit formula for finding the nth term of a sequence that begins with 2, 6, 10, 14,...
What is an = 4n − 2?
This is the function that shows how Jim earns $300 plus 3.5% of his total sales.
What is p(x) = 0.035x + 300?
The function 30,000(0.78)^x models a stock portfolio. What is the yearly percent change?
What is a 22% decrease?
These are the most appropriate kinds of numbers for the domain of the cost of frozen yogurt sold by weight.
What are nonnegative rational numbers?
This is type of equation that represents a rental card decreasing by $2.75 per rental.
What is linear?
This is a cost function for a store showing how the first song costs $1.29 and each additional song costs $0.99.
What is C = 1.29 + 0.99(s − 1)?
This is an equation that represents $1000 compounded annually at 1.3% for 2 years.
What is A = 1000(1 + 0.013)^2?
These are the most appropriate kinds of numbers for the domain of the cost of beef sold by the pound.
What are positive rational numbers?
This is a type of equation used when a pattern does not have a constant rate of change.
What is exponential?
This is how many rental Caitlin can afford if she has $175 and spends $2.75 per rental.
What is 63?
The exponential model of a population triples every 4 years and starts at 5.
What is P(t) = 5(3)^(t/4)?
When f(x) = x^2 − 4, this is f(−3).
What is 5?
The average rate of change per year if a building had 11 households with broadband in 2002 and 23 in 2004.
What is 6 households per year?
Which situation is linear: 7% annual depreciation, bacteria doubling weekly, $50 initial fee plus $30 monthly, or 0.1% monthly growth?
$50 initial fee plus $30 monthly.
The value of 119.67(0.61)^3 − 119.67(0.61)^5 (rounded to the nearest hundredth).
What is 17.06?
This is a type of function with a constant rate of change.
What is a linear function?
A stock value modeled by 30,000(0.78)^x. Does it increase or decrease each year?
Decrease
This term describes a kind of change in a function’s outputs when they are multiplied by 2 each time x increases by 1.
What is the common ratio?