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Exam 5: Exponential and Logarithmic Functions

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Exam 1: Preliminaries205 Questionsadd course
Exam 2: Functions, Limits and the Derivative269 Questionsadd course
Exam 3: Differentiation330 Questionsadd course
Exam 4: Applications of the Derivative182 Questionsadd course
Exam 5: Exponential and Logarithmic Functions278 Questionsadd course
Exam 6: Integration314 Questionsadd course
Exam 7: Additional Topics in Integration250 Questionsadd course
Exam 8: Calculus of Several Variables206 Questionsadd course
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Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent. P = $180,000, r = 6%, t = 5, compounded daily $__________

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Question 121

Find the derivative of the function. Find the derivative of the function.

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Question 122

Express the equation in logarithmic form. Express the equation in logarithmic form.

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Question 123

Use the laws of logarithms to simplify the expression. Use the laws of logarithms to simplify the expression.

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Question 124

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . What is the price of the commodity at ? $ /unit How fast is the price of the commodity changing at ? (increasing / decreasing) at the rate of $ /wk Find the equilibrium price of the commodity. (Hint: It's given by . Also, use the fact that .) $ /unit . What is the price of the commodity at The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . What is the price of the commodity at ? $ /unit How fast is the price of the commodity changing at ? (increasing / decreasing) at the rate of $ /wk Find the equilibrium price of the commodity. (Hint: It's given by . Also, use the fact that .) $ /unit ? $ The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . What is the price of the commodity at ? $ /unit How fast is the price of the commodity changing at ? (increasing / decreasing) at the rate of $ /wk Find the equilibrium price of the commodity. (Hint: It's given by . Also, use the fact that .) $ /unit /unit How fast is the price of the commodity changing at The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . What is the price of the commodity at ? $ /unit How fast is the price of the commodity changing at ? (increasing / decreasing) at the rate of $ /wk Find the equilibrium price of the commodity. (Hint: It's given by . Also, use the fact that .) $ /unit ? The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . What is the price of the commodity at ? $ /unit How fast is the price of the commodity changing at ? (increasing / decreasing) at the rate of $ /wk Find the equilibrium price of the commodity. (Hint: It's given by . Also, use the fact that .) $ /unit (increasing / decreasing) at the rate of $ The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . What is the price of the commodity at ? $ /unit How fast is the price of the commodity changing at ? (increasing / decreasing) at the rate of $ /wk Find the equilibrium price of the commodity. (Hint: It's given by . Also, use the fact that .) $ /unit /wk Find the equilibrium price of the commodity. (Hint: It's given by The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . What is the price of the commodity at ? $ /unit How fast is the price of the commodity changing at ? (increasing / decreasing) at the rate of $ /wk Find the equilibrium price of the commodity. (Hint: It's given by . Also, use the fact that .) $ /unit . Also, use the fact that The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . What is the price of the commodity at ? $ /unit How fast is the price of the commodity changing at ? (increasing / decreasing) at the rate of $ /wk Find the equilibrium price of the commodity. (Hint: It's given by . Also, use the fact that .) $ /unit .) $ The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . What is the price of the commodity at ? $ /unit How fast is the price of the commodity changing at ? (increasing / decreasing) at the rate of $ /wk Find the equilibrium price of the commodity. (Hint: It's given by . Also, use the fact that .) $ /unit /unit

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Question 125

How long will it take an investment of $5,000 to double if the investment earns interest at the rate of 8% / year compounded monthly? Round your answer to the nearest tenth. __________ year(s)

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Question 126

Find the second derivative of the function. Find the second derivative of the function.

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Question 127

Evaluate the expression. Evaluate the expression. = __________ = __________

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Question 128

The strain (percent of compression) on the lumbar vertebral disks in an adult human as a function of the load x (in kilograms) is given by The strain (percent of compression) on the lumbar vertebral disks in an adult human as a function of the load x (in kilograms) is given by . Give the answer to four decimal places. What is the rate of change of the strain with respect to the load when the load is 200 kg? __________ What is the rate of change of the strain with respect to the load when the load is 400 kg? __________ . Give the answer to four decimal places. What is the rate of change of the strain with respect to the load when the load is 200 kg? __________ The strain (percent of compression) on the lumbar vertebral disks in an adult human as a function of the load x (in kilograms) is given by . Give the answer to four decimal places. What is the rate of change of the strain with respect to the load when the load is 200 kg? __________ What is the rate of change of the strain with respect to the load when the load is 400 kg? __________ What is the rate of change of the strain with respect to the load when the load is 400 kg? __________ The strain (percent of compression) on the lumbar vertebral disks in an adult human as a function of the load x (in kilograms) is given by . Give the answer to four decimal places. What is the rate of change of the strain with respect to the load when the load is 200 kg? __________ What is the rate of change of the strain with respect to the load when the load is 400 kg? __________

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Question 129

Sketch the graph of the equation. Sketch the graph of the equation.

(Multiple Choice)
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Question 130

The concentration of a drug in an organ at any time The concentration of a drug in an organ at any time (in seconds) is given by where is measured in grams/cubic centimeter How long would it take for the concentration of the drug in the organ to reach 0.17 How long would it take for the concentration of the drug in the organ to reach 0.16 Round your answer to the nearest hundredth. (in seconds) is given by The concentration of a drug in an organ at any time (in seconds) is given by where is measured in grams/cubic centimeter How long would it take for the concentration of the drug in the organ to reach 0.17 How long would it take for the concentration of the drug in the organ to reach 0.16 Round your answer to the nearest hundredth. where The concentration of a drug in an organ at any time (in seconds) is given by where is measured in grams/cubic centimeter How long would it take for the concentration of the drug in the organ to reach 0.17 How long would it take for the concentration of the drug in the organ to reach 0.16 Round your answer to the nearest hundredth. is measured in grams/cubic centimeter The concentration of a drug in an organ at any time (in seconds) is given by where is measured in grams/cubic centimeter How long would it take for the concentration of the drug in the organ to reach 0.17 How long would it take for the concentration of the drug in the organ to reach 0.16 Round your answer to the nearest hundredth. How long would it take for the concentration of the drug in the organ to reach 0.17 The concentration of a drug in an organ at any time (in seconds) is given by where is measured in grams/cubic centimeter How long would it take for the concentration of the drug in the organ to reach 0.17 How long would it take for the concentration of the drug in the organ to reach 0.16 Round your answer to the nearest hundredth. How long would it take for the concentration of the drug in the organ to reach 0.16 The concentration of a drug in an organ at any time (in seconds) is given by where is measured in grams/cubic centimeter How long would it take for the concentration of the drug in the organ to reach 0.17 How long would it take for the concentration of the drug in the organ to reach 0.16 Round your answer to the nearest hundredth. Round your answer to the nearest hundredth.

(Multiple Choice)
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Question 131

Simplify the expression. Simplify the expression.

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Question 132

Find the derivative of the function. Find the derivative of the function.

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Question 133

Simplify the expression. Simplify the expression.

(Multiple Choice)
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Question 134

Use the curve-sketching guideline, to sketch the graph of the function. Use the curve-sketching guideline, to sketch the graph of the function.

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Question 135

Find the derivative of the function. Find the derivative of the function.

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Question 136

Find the accumulated amount after 4 year(s) if $3,000 is invested at 8% compounded continuously. Round your answer to the nearest cent. $__________

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Question 137

Find the present value of $57,939 due in 6 year(s) at an interest rate of 9% / year compounded continuously. Round your answer to the nearest integer.

(Multiple Choice)
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Question 138

Solve the equation for x. Solve the equation for x.

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Question 139

A women's clothing chain store, found that t days after the end of a sales promotion the volume of sales was given by A women's clothing chain store, found that t days after the end of a sales promotion the volume of sales was given by dollars. Find to the nearest dollar the rate of change of sales volume when t = 1. $__________ dollars. Find to the nearest dollar the rate of change of sales volume when t = 1. $__________

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Question 140
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