Terms
Misc.
Sequence/Arith/Geo/Exp
Evaluate/Solve Equations
Story Problems
100
Is appreciation increasing or decreasing in value?
Increasing
100
Solve the equation for y.
y + 3x = 8x - 7
y = 5x -7
100
Is the sequence arithmetic, geometric or neither?
3, 9, 27, 81
Geometric
100
Solve the system of equations. Write as an ordered pair.
x = 1 – y
3x – y = 11
(3, -2)
100
Write an equation of an exponential function that passes through the points (0, 2) and (2, 18). Using a table and graph may be useful.
y = 2(3)x
Several ways to solve. By table or graph.
or Equal Values Method:
2 = a b0 and 18 = ab2
2 = a and 18/b2 = a
2 = 18/b2 so b2 = 18/2 so b2 = 9 then b = 3
or find multiplier 18/2 = 9, 9 = b*b so b =3
200
Is depreciation increasing or decreasing in value?
Decreasing
200
Write an expression below as an equivalent expression without negative exponents.
(1/2)-3
8
200
Is the sequence arithmetic, geometric or neither?
3, 12, 21, 30 . . .
Arithmetic
200
Evaluate the function f(x) = 2(3)x
for f(-3) =
2/27
200
Amelia deposited $500 in her savings account that earns 5% compounded annually. She forgot about it until 15 years later when she came across an old bank statement. How much will be in her account now?
$1039.46
your multiplier is an increase of 5% so you use 1.05 for the multiplier.
y = 500(1.05)15
300
What kind of function is y = 3x + 5?
Linear
300
Write 8(1/3) in radical form and solve without a calculator.
2
300
Is y = 3(1)x an exponential function? Explain why or why not.
No, because it is linear.
300
Determine the point of intersection of each pair of lines below by using the elimination method. Write answer as an ordered pair.
2x + 3y = 18
2x – 3y = –6
(3, 4)
300
A radioactive isotope is decaying at a rate of 18% every hour. Currently there are 100 grams of the substance. Write an equation that will represent the number of grams present after n hours.
R(n) = 100(0.82)n
So to get your multiplier you must take 1 - .18 which = .82
400
What kind of function is y = 3(.5)x
Exponential
400
I bought a used van for $20,000. If is will decrease in value 15% per year, what is the value of the van in 8 years?
a. Write the equation in y = abx.
b. What is my van worth in 8 years?
a. y = 20000 (.85)x
b. $5449.81
400
For this arithmetic sequence, find the explicit function for t(n).
5, 12, 19, 26 . . .
t(n) = 7n -2
400
Find the product of
(5x + 1)(4x − 2)
20x2 - 6x - 2
400
Write an equation for the exponential growth of population in the U.S. if in 1970 the population was 203 million and ten years later, 1980, the population was 226 million. (So, t(0) = 203 and t(10) = 226.)
P(n) = 203(1.0108)n
One way to solve:
226 = 203 (b)10
divide by 203 on both sides to get
226/203 = b10
so you need to take the 10th root of (226/203)
how you put in calculator is (226/203) = y sq rt button 10 = 1.01079071 which is your multiplier b.
500
What is the multiplier in this equation? Write it as a %.
y = 4(1.75)x
175% or 75% increase
500
Find an exponential function that passes through each pair of points.
(0, 4) and (3, 108)
Hint: 4 = ab0 and 108 = ab3, then solve for a. Use Equal Value Terms to find a and then substitute in to find b. Write in y = a(b)x form.
y = 4 (3)x
500
For this geometric sequence 3, 9, 27, 81 . . .
a. Write the explicit equation for the general term an.
b. Find a6.
a. an = 1*3n or an = 3n
b. a6 = 729
500
Solve the system of equations. Write answer as an ordered pair.
(-30, -94)
500
The price of gas went up by 0.5% last month. Suppose gas currently costs $2.44 a gallon. If the price of gas continues to increase at this rate ... What will it cost one year from now?
$2.59
.5% is .005 and since it is an increase the multiplier will be 1.005. You also need to know that there are 12 months in a year.
y = 2.44 (1.005)12