Geometric Sequence
Growth and Decay
Graphing Exponential Functions
Variety & Word Problems
100
This is the general formula (sometimes called the explicit formula) for a geometric sequence. (Hint: It uses r, n, a1, and an)
What is an = a1(r)(n-1)?
100
Write the operation which replaces the ? to make the exponential growth formula: A = P(1 ? r)^t
What is +? (Or what is addition?)
100
This is the equation graphed below:
What is y = 2x?
100
Mr. Zehnder repeatedly zooms out using his mouse wheel when looking at an image in Desmos because it's very mesmerizing, kind of like Carl. The function f(x) = 3(0.75)^x represents the area of the image after x zoom outs. This is the area of the image after 5 zoom outs (rounded to the nearest tenth).
What is 0.7?
200
These are the next three terms of the geometric sequence: 1,3,9,27...
What are 81, 243, and 729?
200
Bidoof notices the size of his tail grows at a rate of 5% per day. His tail is currently 12 inches long. This is the exponential equation giving his tail length in inches (y) after x days.
What is y = 12(1.05)^x?
200
This is the equation graphed below:
What is y = (1/2)x {or y=0.5x}
200
This is the domain of all exponential functions, linear functions, quadratic functions, absolute value functions, cubic functions, sine & cosine functions, quartic functions, and pretty much any higher power function.
Hint, it's like the only thing domain has ever been so far for the most part.
What is All Real Numbers?
300
The first term of a geometric sequence is 4 and the common ratio is 5. This is it's 10th term.
What is 7,812,500?
300
A population of 1,300 people in 2000 decreases at a rate of 1% until the year 2008. This is the new population in 2008 (Rounded to the nearest person).
What is 1200?
300
This is the equation of the graph below:
What is y = -(2)x?
300
This is the choice of Geometric, Arithmetic, or Neither that describes the following pattern related to the golden ratio, a ratio used in art, photography, and defeating enemy stands:
1, 1, 2, 3, 5, 8, 13, ...
What is neither?
400
This is the answer to the following.
Yes or No, the sequence 9,3,-1,-5 is geometric.
What is no, it is not geometric because there is no common ratio.
400
Sadmep invests $1000 in a savings account at a rate of 3% compounded annual. This is the amount in Sadmep's account after 5 years (Rounded to the nearest cent).
$1159.27
400
This is the equation of the graph below:
What is y = 2x + 1
400
STUDY ISLAND QUESTION: Robert is considering purchasing a working antique brick pizza oven that costs $70,900. If he expects the pizza oven value to decrease 7% each year, which function will show the value of Robert's working antique brick pizza oven after t years?
What is V(t) = $70,900(0.93)t ?
or y = 70900(0.93)t
500
In 2015, 20 ducks lived in a pond. The population grew by 20% each year. This is the number of ducks in the pond in 2021 (rounded to the nearest DUCK).
What is 60 ducks?
Beware the ducks.
500
Write either a growth or decay function for the following information. An antique car is worth $32,000 and its value grows by 7% per year. Find the value after 5 years.
$44881.66
500
This is the equation of the graph below, a translation of y = 3x.
What is y = 3(x-2)?
500
This is the recursive formula in terms of an, an-1, and r for the following geometric sequence:
99, 33, 11, 11/3, 11/9, 11/27, ...
What is an = an-1(1/3)?