Logs
If f(x)=4(3)x, what is the value of f(3)?
108
The altitude of an airplane decreases by 2.5% each minute. If the plane has a current altitude of 17,500 feet, what will be the altitude of the plane 15 minutes later?
11,970 Feet
Factor -2x2 - 5x + 3
(-2x + 1)(x + 3)
Multiply and simplify the product.
x + 5 / x2 + 3x - 28 times x2 - 7x + 12 / x + 7
(x + 5)(x - 3) / (x + 7)2
What is the degree of this polynomial?
x(3x7 + 0.8x10 + 9x3)
11
Sanjay checked his screen time and discovered he was using technology an average of 6 hours per day. The equation y=6(0.75)x estimates Sanjay’s daily screen time x weeks after noticing the trend. What does the number 0.75 tell us about the trend of Sanjay’s screen time usage?
He decreased his time by 25%.
An initial deposit of $2200 is invested in an account that pays 3.8% annual interest, compounded annually. How long will it take until the balance grows to $5000?
22.02 years
Factor 3x2 + 5x - 2
(3x - 1)(x + 2)
ADD:
2 / x - 1 PLUS 4x - 1 / x2 + 4x - 5
6x + 9 / x2 + 4x - 5
Imagine a graph in the shape of a capital letter M on a coordinate plane. What is the degree of this graph?
4
Solve 24x-2 = 1024 for x
x = 3
Which statement models an exponential relationship?
a) reading 20 more pages of a book every night
b) getting a $500 raise every six months
c) a bank account balance increasing by 10% each month
d) a bank account increasing by $10 each month
C - an increase of 10% each month
How does y = -2/3 (x + 7)2 - 4 transform from the graph of y = x2?
List three ways.
It has a MAXIMUM, it is 7 left, and 4 down. The 2/3 makes it wider.
SUBTRACT
5x / 2 MINUS x + 1 / 2x - 4
5x2 - 11 x - 1 / 2x - 4
What is the domain and range of the graph you see on the board?
Domain: x > or equal to -2
Range: y > or equal to -1
Solve 8log4(x - 7) = 16 for x
x = 23
A cup of coffee is measured to be 185oF. If left alone, the temp of the coffee decreases by 3.5% each minute. What would be the temp if left alone for 20 minutes?
About 91oF
Multiply (2 - 5i)(-3 + 4i)
14 + 23i
f(x) = 3x + 6 / 4x - 20 g(x) = 9x + 9 / 2x - 10
What is f(x) divided by g(x)?
(x + 2) / (6x + 6)
What are all of the zeros of this function?
y = (x + 5)(-3x - 7)(4x + 2)(x + 2)(-3x - 10)
x = -5, 7/3, -1/2, -2, 10/3
Solve 288 = 3x + 45 for x.
x = 5
Invest $10,000 for 10 years at a rate of 3.25%, compounded yearly. What is the balance after 10 years?
$13,768.94
On the board, draw a quadratic graph that points down from the point (2, -6). Call it f(x). If this graph is transformed to g(x), and has TWO real solutions, which could have taken place?
a) a vertical stretch by a factor of 2 b) a vertical shift UP 8 units
c) a vertical shift up 5 units d) a reflection across the x axis
B - a vertical shift up 8
See the board....
x + 6 / x + 5
Factor: 16 - 2x3
2(8 - x3)= 2(2 - x)(4 + 2x + x2)