Growth & Decay
An exponential function is a function with the variable as the __________________
exponent
Convert the following to LOG form
3^x = 8
log3 8 = x
What is the domain of exponential functions?
All real numbers
Expand log5 (17x2)
log517 + 2log5x
Solve
0.5x=22x+7
x = -7/3
What is the exponential growth formula?
y = a(1+r)^t
Convert the following to exponential form
log6 13 = n
6n=13
What is the range of logarithmic functions?
All real numbers
Condense
log3 67 - 2 log3x + log3y
log3 (67y/x2)
Solve
9x-2=273x
x= -4/7
Tom buys car for $40,300. It depreciates in value at a rate of 17% each year. What is the value of the car after 5 years.
$15,874.33
Evaluate
log2128
What is the inverse of y = 2x
log2x
Expand
log52x4
Solve
log6(5x - x2)=log6(2x - 4)
x = 4
x = -1 is extraneous
Joe deposited $11,600 in an account that pays 1.75% interest. Find the balance after 3 years if the interest is compounded quarterly.
$12,223.87
Given the logarithms below, which one does not equal the others?
log341 ln 1
log671 log 10
log 10 is 1 and the others have a value of 0
What type of asymptotes do exponential functions have? (vertical or horizontal)
horizontal asymptote
Condense
1/3log4x + log4y + 5log4z
log4 (x1/3yz5)
Solve
log24 + log2x = 6
x=16
Olivia has inherited land from her grandma. She decided the sell the land for $130,000 then place the money in a new account that earns 1.8% interest compounded monthly. How much interest will she have earned after 10 years?
$25,617.27
Given: log48 = a and log45 = b, which expression is equivalent to 40?
A) 4a + 4b B) 4ab C) 16ab
D) 4a+b E) 16ab F) 16a+b
D
What is the domain of y = log1/3x
x>0
Condense
logx - 2logy + 3logz
log (xz^3/y^2)
Solve
5x+3=10
x = -1.57