Exponential Functions
Determine whether the function represents an exponential growth or decay.
f(x)=(3/4)^x
Exponential Decay
Solve the equation.
3^(x+4)=81
x = 0
Rewrite the equation in logarithmic form.
14^2=196
log14196 = 2
Solve
log(3x + 3) = log(5x + 1)
x = 1
Rewrite in exponential form:
Log 3(2x) = 7
37 = 2x
Solve the equation.
(Give the exact value that you would type in the calculator)
4e^(2x+1)=12
(-1+ln3)/2
Evaluate the logarithm with a calculator.
log1664
1.5
Solve
log2(x - 3) = 5
x = 35
What is the equation of the asymptote for
f(x) = 3x-4 + 2
y = 2
Solve the exponential equation.
5^(3x+1)*5^(2x-5)=5^(x+6)
x=10/4
Evaluate the logarithm without a calculator.
log749
2
Solve:
log3(x) + log3(x - 2) = 1
x = 3
What is the domain and range for
g(x) = (1/2)x+1 + 3
domain: (-inf, inf)
Range: (3, inf)
Solve for x:
4^(x-2)=16^(2x+1)
x=-4/3
Condense the logarithmic expression.
5lnx-4lny+2lnz
ln(x5z2/y4)
Solve. Check for extraneous solutions.
log9(6-3w) = log9(-2w)
No Solution
Find the ending amount of an investment of $10000 invested at 4% interest compounded monthly for 5 years.
f(t)=a(1+r/n)^(nt)
$12,209.97
How many years would it take for a balance to reach with an initial payment of $5000.00 with a 3% interest rate compounded quarterly?
(Solve for t)
25000 = 5000(1 + .03/4)4t
t = 54 years
What is the domain and range for
f(x) = log2(x + 3)
domain: (-3, inf)
range: (-inf, inf)
Solve for p.
log36(20-4p)=1/2
p = 7/2