Exponential Functions
If $5400 is invested at an interest rate of 3.5% per year, compounded continuously, find the value of the investment after 2 years.
What is $5791.54?
Express the equation in exponential form
ln 5 = 3y
ln(t+1) = -1
What is 5=e^{3y}?
What is t=e^{-1} -1?
Use laws of logarithms to evaluate the expression
log_3(100) - log_3(18) - log_3(50)
What is -2?
Find the solution of the exponential equation
e^{1-2x} = e^{4x-7}
What is 4/3?
The half-life of strontium-90 is 28 years. How long will it take a 50-mg sample to decay to a mass of 32 mg?
What is 18 years?
If $750 is invested at an interest rate of 3.75% per year, compounded quarterly, find the value of the investment after 5 years.
What is $903.88?
Express the equation in logarithmic form
3^{2x}=10
10^{-4x}=0.1
What is x=1/2(log_3(10))?
What is x=1/4?
Use the Laws of Logarithms to expand the expression
log(AB^2)
What is log A + 2log B?
Find the exact solution of the exponential equation in terms of logarithms.
2(5+3^{x+1})=100
What is log_3(45) - 1?
A roasted turkey is taken from an oven when its temperature has reached 185F and is placed on a table in a room where the temperature is 75F.
(a) If the temperature of the turkey is 150F after half an hour, what is its temperature after 45 min?
(b) After how many hours will the turkey cool to 100F?
What is 137F?
What is 2 hours?
Find the present value of $100,000 if interest is paid at a rate of 8% per year, compounded monthly, for 5 years.
What is $67,121.04?
Find the domain of the following function
f(x)=log_5(8-2x)
What is x<4?
Simplify the following expression
e^{2x}*e^{3y}*e^{-7z}
What is e^{2x+3y}/e^{7z}?
Solve the equation
e^{4x}+4e^{2x}-21=0
What is x=0.5493?
The pH of lime juice is 1.9. Find the hydrogen ion concentration.
What is 10^{-1.9}?
If $925 is invested at an interest rate of 2.5% per year, find the amount of the investment at the end of 10 years, given that it is being compounded semiannually.
What is $1185.88?
Find the domain of the function
f(x)=ln(4-x^2)
What is (-2,2)?
Use the Change of Base Formula to show that
log e = 1/ln(10)
What is log e = 1/ln(10)?
Solve the equation
x^2 * 2^x - 2^x = 0
What is x=+/- 1?
If one earthquake has magnitude 6.5 on the Richter scale, what is the magnitude of another quake that is 35 times as intense?
What is 8.0?
A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t)=13e^{-0.015t}, where m(t) is measured in kilograms.
(a) Find the mass at time t = 0.
(b) How much of the mass remains after 45 days?
What is 13 kg?
What is 6.62 kg?
Find the inverse of the function
f(x) = 2^x/(1+2^x)
What is log_2(x/1-x)?
Use the Laws of Logarithms to combine the expression.
3 ln 2 + 2 ln x - 1/2(ln(x+4))
What is ln(8x/(x+4)^1/2)?
Solve for x
ln(x-1/2)+ln(2)=2ln(x)
What is x =1?
The drilling of a jackhammer was measured at 132 dB. The sound of whispering was measured at 28 dB. Find the ratio of the intensity of the drilling to that of the whispering.
What is 2.5 x 10^10?