Exam 5: Exponential and Logarithmic Functions

On the Richter scale, the magnitude R of an earthquake is given by the formula where I is the intensity of the earthquake being measured and I₀ is the standard reference intensity. Suppose an earthquake is measured with a magnitude of 5 on the Richter scale with an error of at most 2%. Use differentials to find the error in the intensity of the earthquake. Round your answer to the nearest integer. ​

Find the second derivative of the function. ​ ​

The concentration of a drug in an organ at any time t (in seconds) is given by where is measured in grams/cubic centimeter . ​ Please round the answer to two decimal places. ​ How long would it take for the concentration of the drug in the organ to reach 0.17 ? ​ t = __________ sec ​ How long would it take for the concentration of the drug in the organ to reach 0.15 ? ​ t = __________ sec

Find the inflection points of the function . ​

Find the derivative of the function. ​

Find the derivative of the function. ​

Sketch the graph of the equation. ​ ​

The U.S. population is approximated by the function where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2020 ( t = 3 )? ​

Use logarithms to solve the equation for t. ​

The concentration of a drug in an organ at any time t (in seconds) is given by where is measured in grams/cubic centimeter . ​ Round your answer to the nearest hundredth. ​ How long would it take for the concentration of the drug in the organ to reach 0.19 ? ​ __________ seconds ​ How long would it take for the concentration of the drug in the organ to reach 0.12 ? ​ __________ seconds

How long will it take $3,000 to grow to $8,500 if the investment earns interest at the rate of 18% / year compounded monthly? Round your answer to the nearest tenth. ​ __________ year(s)

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 . ​ What is the rate of change of the strain with respect to the load when the load is 50 kg? When the load is 300 kg? Give the answers to four decimal places. ​

Use logarithmic differentiation to find the derivative of the function. ​ ​

Find the second derivative of the function. ​

The monthly demand for a certain brand of table wine is given by the demand equation ​ where p denotes the wholesale price per case (in dollars) and x denotes the number of cases demanded. ​ Find the rate of change of the price to the nearest hundredth of a cent per case when x = 1,000. ​ __________ cents per case ​ What is the price per case when x = 1,000. ​ $__________ / case

Find the derivative of the function. ​ ​