Word Problems
The concentration C(t)C(t) of a certain drug in the bloodstream after t minutes is given by the formula C(t)=0.07(1−e−0.2t). What is the concentration after 1010 minutes? Round to three decimal places.
0.061
Suppose that y varies inversely as the square of x, and that y = 4 when x = 3x. What is y when x =14? Round your answer to two decimal places if necessary.
0.18
Solve the following elementary exponential equation:
25-x = 5
x = -1/2
Write the following logarithmic equation as an exponential equation. Do not simplify your answer.
ln6 = 4x
e4x = 6
Dolores invests $8100 in a new savings account that earns 3.0% annual interest, compounded continuously. What will be the value of her investment after 3 years? Round to the nearest cent.
8862.81
Hooke's Law says that the force exerted by the spring in a spring scale varies directly with the distance that the spring is stretched. If a 1919 pound mass suspended on a spring scale stretches the spring 55 inches, how far will a 2727 pound mass stretch the spring? Round your answer to one decimal place if necessary.
7.1
Suppose that y is inversely proportional to the cube of x, and that y = 14 when x = 19. What is y when x =13? Round your answer to two decimal places if necessary.
43.71
Solve the following elementary exponential exponential equation:
1000-x = 108x-3
x = 3/11
Evaluate the logarithmic expression w/o the use of a calculator:
log14(196)
x = 2
Tyra invests $9100 in a new savings account which earns 5.1% annual interest, compounded monthly. What will the value of her investment be in 2 years? Round to the nearest cent.
1007.01
The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, V. The lift of a wing with an area of 260 square feet is 39,500 pounds when the plane is going at 90 mph. Find the lifting force if the speed is 240 mph.
Hint: use F=KAV2
F = 280889
Suppose that y varies directly as the square root of x, and that y = 41 when x = 16. What is y when x = 241?
159.12
Solve the following elementary exponential equation"
23x-7 = 1/4
x = 5/3
Write the following equation in logarithmic terms:
7ex = 3
ex = log73
Eva invests $6400 in a new savings account which earns 3.4% annual interest, compounded continuously. What will be the value of her investment after 66 years? Round to the nearest cent.
$7848.31
The function, c(t) = c0(1+r)t models the rise in the cost of a product that has a cost of c0 today, subject to an average yearly inflation rate of r for t years. If the average annual rate of inflation over the next 8 years is assumed to be 2.5%, what will the inflation adjusted cost of a $24,400 motorcycle be in 8 years? Round to 2 decimal places.
c(8) = 29729.03
Suppose that y is inversely proportional to the 4th power of x, and that y = 12 when x = 3. What is y when x = 6?
0.75
Solve the following elementary exponential equation:
64x - 8 = 0
x = 1/2
Evaluate the logarithmic expression w/o the use of a calculator:
log1/4(16)
x = -2
Melanie invests $7600 in a new savings account which earns 4.0% annual interest, compounded monthly. What will be the value of her investment after 22 years? Round to the nearest cent.
18,296.04
A pretzel vendor has determined that the number of pretzels he sells per day is inversely proportional to the price he charges. The vendor wants to decide if increasing his price by 65 cents will drive away too many customers. On average, he sells 145 pretzels a day at a price of $3.45 per pretzel. How many pretzels can he expect to sell if the price is increased by 65 cents?
122 pretzels
The variable a is jointly proportional to the square of b and the square of c. If a = 427, b = 4 and c = 7, what is the value of a when b = 7 and c = 8? Round your answer to two decimal places if necessary.
1708
Statistics show that the fractional part of a pair of flashlight batteries, P, that is still good after t hours of use is given by P=4−0.02t. What fractional part of the batteries is still operating after 150 hours of use? Express your answer as a fraction or as a decimal rounded to six decimal places.
1/64
Write the following logarithmic equation as an exponential equation. Do not simplify your answer.
log351225 = 2
352 = 1225
Erin invests $5100 in a new savings account which earns 4.8% annual interest, compounded continuously. What will be the value of her investment after 22 years? Round to the nearest cent.
$14661.73