What is
b^m • b^n = b^(m+n)
b^m / b^n = b^(m-n)
(b^m)^n = b^(mn)
100
If regular gasoline is selling for $3.95 per gallon, the price of any particular purchase p is a function of the number of gallons g in that purchase, write this as a function then find its inverse.
What is
Function: p=3.95•g
Inverse: g=p/3.95
100
The common multiple of 10, -5, 5/2, -5/4...
What is -1/2
100
The common difference of 5/2, 8/3, 17/6...
What is 1/6
200
General change of base formula
What is log (input)/log (x)
200
rewrite 12^5=248832 in logarithmic for
What is Log 248832 = 5 [Log is base 12]
200
The first 7 digits of pi after 3.14
What is 3.141592653
200
Explicit formula for 10, -5, 5/2, -5/4...
an=10*(-1/2)^(n-1)
200
The explicit equation for 5/2, 8/3, 17/6...
What is an=5/2+(1/3)(n-1)
300
List all logarithm properties
What is
log(mn)=log(m)+log(n)
log(m/n)=log(m)-log(n)
log(m^n)=n•log(m)
300
Solve for x log(x+2) = 7
Note: log is base 4
What is 16382
300
Three ways you could check that your function and its inverse are indeed inverses
Possibilities:
composition of functions = x
coordinates switch (x,y) -> (y,x)
y=x is axis of symmetry
domain and range flip
300
The explicit and recursive general forms
Giddings will judge
Go Blue!
300
The explicit and recursive general forms
Go Blue!
400
Expand: Log ( (x+2)^3 / (3x)^(1/2) )
What is 3Log (x+2) - .5 Log 3 - .5 Log x
400
Mr. Giddings recently purchased a house for $225,000. Houses in his neighborhood appreciate in value continuously by 1%. In 25 years what will Mr. Giddings’s house be worth
What is
225000*e^(.01*25)=$288906
400
The inverse of f(x)=3x^7+1
What is [(x-1)/3]^(1/7)
400
Summation of the first 12 terms of the sequence beginning 10, -5, 5/2, -5/4...
What is 6825/1024 or 6.66504
400
The summation of the first 12 terms of the sequence beginning 5/2, 8/3, 17/6...
What is 41 (also know as Glen Rice's uniform number when he was Big Ten Player of the year and lead Michigan to the 1989 NCAA Basketball Championship!)
500
Solve for x: 3•5^(3x) = 531
What is 1.07204
Also written with log base 5 [Log(531/3)] /3
500
Given an initial investment of $40,000 with a nominal interest of 5% compounded monthly, how many years would it take for your money to be greater $120,000
What is 22.018 years
500
Find the inverse of 5+7•e^(3x+1)=y
What is ([ln ((x-5)/7)]-1)/3
500
The summation of the infinite series beginning 12, 9/2, 27/16...
What is 96/5 = 19.2
500
Why can you not have an infinite arithmetic series, but you can have an infinite geometric sequence?
Only geometric series with a common multiple |d|<1 will converge