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Graphing
Interest Problems
Logarithms
Properties
Exponentials
100
What is a vertical asymptote?
It is an imaginary line in an exponential growth or decay function that the graph approaches but never touches
100

What is the equation for exponential growth?

A = a*(1+r)^t

100

What is the difference between a common logarithm and a natural logarithm?

A natural logarithm is a logarithm with a base of e and common logarithm has a base of 10

100
What is the product property of logaritms
Log base(b) mn = log base(b) m + log base(b) n
100
Simplify the expression e^3(e^4)
e^7
200

Which kind of exponential function approaches zero when not transformed?

Exponential Decay Functions

200

For what values of the entire quantity (1-r) in the equation for exponential decay actually makes the final result less than the initial amount?

Any value less than 1 makes it an exponential decay problem. If it is greater than 1, it is actually an exponential growth problem.

200
Simplfy the expression log 100
2
200
What is the quotient property of logarithms?
log base(b) m/n = log base(b) m - log base(b) n
200

What is the decimal approximation of "e" to three decimal places and to what number set does it belong?

2.718 (and is an irrational number)

300

What is the parent function of y= 5(4^x) + 2

y=b^x   or (an exponential growth function)

300

What is the equation for compound interest?

A=P(1+r/n)^nt

300

What value makes ln(9) = ln(72) - xln(2) true? 

x=3

300
What is the power propety of logaritms
log base(b) m^n = n log base(b) m
300
Is f(x)=1/3e^4x a exponential decay or growth function?
Exponential Growth
400

What is the asymptote for y = log base 2 of (x-3)? Make sure to include x=? or y=?

x=0

400
What is the equation for the amount Mary-Kate will have in her bank acount if she invests  $5,000 and it grows at a rate of 2.3% over 15 years?

A(15) = 5,000*(1.023)^15

400

Please expand log(16/10). Answer should be simplified, if possible. 

log of 16 minus 1

400
What is the change of base formula?

log base b of m = log m / log b

400

Solve 4*ln(w) + 6 = 12

w  = e^(3/2)

500

What is the asymptote for y = 5*3^(x+2) - 4 (include x= or y=)

y = -4

500

What is the equation for how much Evan pays for a loan that is compounded semi-monthly, if it was for $30,000 and has an interest rate of 4%?

A(t) = 30,000*(1+(0.04/24))^24t
500

Solve log base 2 of (6x-15) = log base 2 of (41-2x)

x=7

500

What is the conversion formula between logarithmic and exponential functions?

log base b of m = n   is equal to  b^n = m

500

Solve 9^(x-8) = (1/27)^2x

x=2