Section 4.1
A bacteria culture contains 1500 bacteria initially and doubles every hour.
Find a function N that models the number of bacteria after t hours.
What is N(t)= 1500 x 2t ?
When a certain medical drug is administered to a patient, the number of milligrams remaining in the patient's bloodstream after t hours is modeled by D(t) = 50e-0.2t
How many milligrams of the drug remain in the patient's bloodstream after 3 hours?
What is 27.4 mg?
Express the equation in exponential form.
log7(3y) = 2
What is 72 = 3y?
Assume f is a one-to-one function.
If f-1(3) = -1, find f(-1).
What is 3?
Evaluate the expression.
log2 6- log2 15 + log2 20
What is 3?
A bacteria culture contains 1500 bacteria initially and doubles every hour.
Find the number of bacteria after 24 hours.
A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is proportional to her velocity, and the constant of proportionality is 0.2. It can be shown that the downward velocity of the sky diver at time t is given by v(t) = 180(1- e-0.2t). t=(seconds-s) v(t)= (ft/s).
Find the initial velocity of the sky diver.
what is 0?
Express the equation in exponential form.
ln(t+1)= -1
What is e-1 = t + 1?
if f(x) = 5 - 2x, find f-1(3).
What is 1?
Solve for x.
log x + log(x - 1) = log(4x)
What is 5?
To obtain the graph of g(x) = 2x - 1, we start with the graph of f(x) = 2x and shift it _____ (upward/downward) 1 unit.
What is downward?
A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is proportional to her velocity, and the constant of proportionality is 0.2. It can be shown that the downward velocity of the sky diver at time t is given by v(t) = 180(1- e-0.2t). t=(seconds-s) v(t)= (ft/s).
Find the velocity after 5 and after 10 seconds.
What is 113.8 ft/s and 155.6 ft/s?
Express the equation in logarithmic form.
4x = 70
What is log470= x?
Find the inverse function of f.
f(x) = 3x + 5
What is f-1(x)= 1/3x - 5/3?
Expand the expression.
log5 (3x2/y3)
What is log5 3 + 2log5 x - 3 log5 y ?
To obtain the graph of g(x) = 2x - 1, we start with the graph of f(x) = 2x and shift it to the ________ (left/right) 1 unit.
If $2000 is invested at an interest rate of 3.5% per year, compounded continuously, find the value of the investment after 2 years.
What is $2145.02?
Solve for x.
logx 8 = 3/2
What is 4?
Find the inverse function of f.
f(x) = 5 - 4x3
Combine the expression.
1/3log(x + 2)3 + 1/2[log x4 - log(x2 - x - 6)2]
log(x2 / x-3)
If $500 is invested at an interest rate of 3.75% per year, compounded quarterly, find the value of the investment after 2 years.
If $600 is invested at an interest rate of 2.5% per year, find the amount of the investment at the end of 10 years when compounded semiannually.
What is $769.22?
Evaluate the expression.
log6 36
What is 2?
Find the inverse function of f.
f(x)=1/(x+2)
What is f-1(x) = (1/x)- 2?
If a man invests $5000 in an account that pays 8.5% interest per year, compounded quarterly, how long will it take for the investment to double?
What is 8.24 years?