Exponentials
Which are exponential functions?
3x x5 -24 xx
3x
Solve without a calculator
log2(8)=y
y=3
Solve without a calculator
ln(e3)=y
y=3
What is the n value for compounding:
Monthly?
Yearly?
Quarterly?
Monthly=12
Yearly=1
Quarterly=4
What is your first step to finding an inverse?
Switch the x and y in the function
Solve without a calculator
53=5x
x=3
Solve without a calculator
log4x=2
x=16
Simplify using log/ln rules
ln(x4)
4ln(x)
Set up the equation to measure the amount of money in an account over time if you invest $5000 compounded monthly at a 7% interest rate
A=5000(1+.07/12)^(12t)
What is the inverse of:
y=2x+4
y=(x-4)/2
2x=16
x=4
Solve without a calculator
log(x)=3
x=103 = 1000
Simplify using log/ln rules
ln(x/5)
ln(x)-ln(5)
Find the amount of money accumulated if you invest $1500 at a 7% interest rate for 6 years compounded annually.
$2251.10
What is the inverse of:
y=2x^4-3
y=root(4)((x+3)/2
(1/2)^x=1/8
x=3
Solve without a calculator
logb(36)=2
b=6
Put into condensed form
2ln(x)-4ln(2)
ln(x^2/2^4)
Compound interest Yearly for 5 years on $10,000 at 20% interest. Suppose I deposit this money into an interest bearing account in 2012 and want to know how much it will be worth at the end of 2017. How much would it be worth?
$24,883
Verify the following are inverses:
y=5x-3
y=(x+3)/5
y=5((x+3)/5)-3
(x+3)-3
x
Solve without a calculator
ex=5
x=ln(5)
Solve without a calculator
logx+4(64)=2
x=4
Simplify
ln(e^2/2)
ln(e^2)-ln(2)
2ln(e)-ln(2)
2-ln(2)
If someone invests $15,000 into an account with a 8% interest rate compounded monthly, how long will it be until the account contains $45,000?
13.78 years
Verify the following are inverses:
y=(x-2)^3+4
y=root(3)(x-4)+2
((root(3)(x-4)+2)-2)^3+4
(root(3)(x-4))^3+4
(x-4)+4
x