Finals Session MATH 1111

Section 4.1

100

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 2^t ?

200

A bacteria culture contains 1500 bacteria initially and doubles every hour. 

Find the number of bacteria after 24 hours.

What is 25,165,824,000?

300

To obtain the graph of g(x) = 2^x - 1, we start with the graph of f(x) = 2^x and shift it _____ (upward/downward) 1 unit. 

What is downward?

400

To obtain the graph of g(x) = 2^x - 1, we start with the graph of f(x) = 2^x and shift it to the ________ (left/right) 1 unit.

what is right?

500

If $500 is invested at an interest rate of 3.75% per year, compounded quarterly, find the value of the investment after 2 years.

What is $538.75?

Section 4.2

100

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?

200

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?

300

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?

400

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?

500

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?

Section 4.3

100

Express the equation in exponential form.

log₇(3y) = 2

What is 7² = 3y?

200

Express the equation in exponential form.

ln(t+1)= -1

What is e^-1 = t + 1?

300

Express the equation in logarithmic form.

4^x = 70

What is log₄70= x?

400

Solve for x.

log_x 8 = 3/2

What is 4?

500

Evaluate the expression.

log₆ 36

What is 2?

Section 2.8

100

Assume f is a one-to-one function.

If f^-1(3) = -1, find f(-1).

What is 3?

200

if f(x) = 5 - 2x, find f^-1(3).

What is 1?

300

Find the inverse function of f. 

f(x) = 3x + 5

What is f^-1(x)= 1/3x - 5/3?

400

Find the inverse function of f.

f(x) = 5 - 4x³

What is f^-1(x) = cuberoot of 1/4(5-x)?

500

Find the inverse function of f.

f(x)=1/(x+2)

What is f^-1(x) = (1/x)- 2?

Section 4.4 and 4.5

100

Evaluate the expression.

log₂ 6- log₂ 15 + log₂ 20

What is 3?

200

Solve for x. 

log x + log(x - 1) = log(4x)

What is 5?

300

Expand the expression.

log₅ (3x²/y³)

What is log₅ 3 + 2log₅ x - 3 log₅ y ?

400

Combine the expression.

1/3log(x + 2)³ + 1/2[log x⁴ - log(x² - x - 6)²]

log(x² / x-3)

500

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?