Quadratics
What are 4 ways you can solve a quadratic?
The quadratic equation, factoring, graphing, and completing the square.
What is the difference between an arithmetic and geometric sequence?
Arithmetic sequences change by a constant difference each time, while geometric sequences change by a constant ratio each time.
What is the compound interest formula?
A=P(1+r/n)nt
Which part of the exponential equation tells you if it is a growth or decay?
(1+r) = growth
(1-r)= decay
What do you do when you have a negative exponent?
You bring it to the denominator.
ex) 2-5=1/25
Solve the equation using factoring.
n2 + 3n - 18 =0
(n+6) (n-3)
n= {-6,3)
What is this formula?
an=r x an-1
It is a recursive geometric sequence formula.
What is the difference between simple and compound interest?
Simple interest is calculated on the original amount. Compound interest is calculated on the original amount AND the accumulated interest.
What is the Asymptote?
When the graph approaches the x-axis, but never touches it.
What do you do when you have a fractional exponent?
The numerator is the power, and the denominator is the root.
ex) xm/n=n√(xm)
Solve the equation using the quadratic formula.
2x² - 3x - 5 = 0
x = 5/2 and x = -1
x={5/2, -1}
A library has a bookshelf with books. The first shelf has 15 books, and each shelf below it has 2 fewer books than the shelf above it. How many books are on the 5th shelf?
The 5th shelf has 7 books
You invested 52,400 at 6% compounded annually for 5 years. What is your total return of the investment?
What is the difference between a growth rate and growth factor?
Growth rate is the percentage, and growth factor is the multiplier/decimal.
16-3/2=?
1/64
A relief package is released from a helicopter at 1600 feet. The height of the package can be modeled by the equation h=-16t2 + 1600, where h is the height of the package in feet and t is the time in seconds. The pilot wants to know how long it will take for the package to hit the ground.
10 seconds
Given the first term and the common ratio of a geometric sequence find the recursive formula and the three terms in the sequence after the last one given.
a1 = 4, r = 6
Next 3 terms: 24, 144, 864
Recursive: an = an-1 ⋅ 6
a1 = 4
Sam invested $6,000 in two bank accounts. One of the accounts pays 4% interest per semi-annually, and the other account pays 10% interest per year. If Sam left the money in account 1 for 12 years, and the money in account 2 for 8 years, which account would have more, and what is the difference?
Account 2 has $3,210.91 more than account 1.
Ms. Cohen's garden had 50 weeds when she began spraying her garden with pesticide. Every day she sprayed pesticide there were half as many weeds as the day before. Write an equation that models this situation.
(Let x = # of days and y = # of weeds)
y=50(0.5)x
Find the area of a rectangle with the length of 8a3b2 and the width of 7a5b4
56a8b6
A ball is shot from a cannon into the air with an upward velocity of 40 ft/sec. The equation that gives the height (h) of the ball at any time (t) is: h(t)= -16t2 + 40t + 1.5. How long does it take the ball to reach a height of 20 feet? Round to the nearest hundredth.
0.61 seconds and 1.89 seconds.
A store offers a 20% discount on an item each day. If the initial price is $100. If the price after one day is $80, then what is the cost after 5 days?
$32.77
Shawn is buying a new Jet Ski for $12,500. He is considering 2 credit options. Option A offers a 6 year loan with 8.5% interest compounded quarterly, while Option B offers a 5 year loan with 10% interest compounded annually. Which option is better?
Option A
Marty the Marmoset wants to save money to buy a really big present for their longtime sweetheart, Dana the Dugong. Right now Marty has $1500, and knows the local River Bank will give them 3.75% on any investments, and Marty knows they want to buy the gift in five years.
Write an exponential growth model to represent this situation, and use it to figure out how much money Marty will have to buy Dana a present.
A=1500(1+0.0375)t
$1803.15
93x-2= 6561
2