3.1 Exponential Functions
Describe the transformation of the graph of f(x) to g(x)
f(x) = 4^x
g(x)= 4^(x-2) - 3
What is right 2 units and down 3 units?
Rewrite the logarithm in exponential form.
log_10(1/1000)=-3
What is
10^(-3)=1/1000
Evaluate the logarithm using the change-of-base formula.
log_(1/2) 9
What is -3.170?
Solve for x.
3^(x-1)=1/81
What is -3?
The first person to stand on their chair and say my turtle's name correctly wins the points for their team.
Using a calculator, estimate the function at x = 0.02. Round to the nearest thousandth
g(x) = 50 e^(4x)
What is 54.164?
Rewrite the exponential equation in logarithmic form.
3^5=243
What is
log_3 243= 5
Simplify
ln sqrt(e^5)
What is
5/2
Solve for x.
log_10 x^2=6
What is 1000?
How many years would it take to double an investment of $5,000 at an interest rate of 4% compounded continuously?
What is 17.33 years?
The formula below gives the balance A of an account earning what type of interest?
A = P e^(rt)
What is continuous compounding?
Rewrite the exponential equation in logarithmic form.
1/(e^4)=0.0183
What is
ln 0.0183 = -4
Evaluate
log_5 75 - log_5 3
What is 2?
Solve for x.
ln(3x+5)=8
What is
(e^8-5)/3
How many years would it take to triple an investment of $3,000 at an interest rate of 2% compounded continuously.
What is 54.93 years?
The balance of an account in which you invested $100 at an annual interest rate of 5% after 4 year compounded monthly.
What is $122.09
Solve by converting to exponential form.
log_5 125= x
What is x = 3?
Expand the logarithmic expression
ln (sqrt(x)/4)
What is
1/2 ln x -ln 4
Solve for x.
e^(2x)-5e^x+6=0
What are x=ln (3) and x = ln(2)?
Practice Test Question 15, just the average.
What is 74?
A new SUV costs $32,000. The value V of the SUV after t years is modeled below.
V(t) = 32,000(3/4)^(t)
1. Use the model to graph the function. When does the SUV depreciate most rapidly? Is this realistic? Explain.
2. What is the value of the SUV after 2 years?
What is...
1) When it is first sold; Yes it is realistic.
2) $18,000
The domain of the logarithmic function (in interval notation)?
What is
(0, oo)
Condense the logarithmic expression.
3[ln x- 2ln(x^2 +1)]+ 2 ln 5
What is
ln ((25x^3)/(x^2+1)^6)
Solve for x.
x ln(x) +x=0
What is 0.368?
Practice Test Question 14
What is k = 0.0177 and 11,407,330?