Exam 5: Exponential and Logarithmic Functions

Solve the equation for . ​ ​

Find the derivative of the function. ​

Find the second derivative of the function. ​

Find the second derivative of the function. ​ ​

Simplify the expression. ​

Find the interest rate needed for an investment of $6,000 to grow to an amount of $7,000 in 3 year(s) if interest is compounded continuously. Round your answer to two decimal places. ​

How long will it take $4,000 to grow to $7,500 if the investment earns interest at the rate of 14% / year compounded monthly? Round your answer to one decimal place. ​

Given that a quantity Q(t) is described by the exponential growth function where t is measured in minutes. What is the growth constant? What quantity is present initially? Complete the table of values. Round your answers to the nearest integer. t

Bernie invested a sum of money 5 year(s) ago in a savings account, which has since paid interest at the rate of 6% / year compounded quarterly. His investment is now worth $22,927.66. How much did he originally invest? Round your answer to the nearest cent. ​ $__________

Find the derivative of the function. ​ ​

Find the derivative of the function. ​ ​

The monthly demand for a certain brand of perfume is given by the demand equation where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded. ​ Find the rate of change of the price to the nearest hundredth of a cent per bottle when x = 2,000. ​ __________ cents per bottle ​ What is the price per bottle when x = 2,000. ​ $__________ / bottle

Evaluate the expression. ​ __________

Find the derivative of the function. ​

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 = $2,400, r = 6%, t = 10, compounded semiannually ​

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 = 2. ​ $__________

The height (in feet) of a certain kind of tree is approximated by where t is the age of the tree in years. Estimate the age of a 60-ft tree. Please round the answer to two decimal places. ​ t = __________ years

Simplify the expression. ​ ​

Skeletal remains of the so-called "Pittsburgh Man", unearthed in Pennsylvania, had lost 74% of the carbon 14 they originally contained. Determine the approximate age of the bones. Round your answer to the nearest year.

The concentration of a drug in an organ at any time (in seconds) is given by ​ ​ where is measured in milligrams/cubic centimeter (mg/cm³). ​ What is the initial concentration of the drug in the organ? ​ __________mg/cm³ ​ What is the concentration to four decimal places of the drug in the organ after 10 sec? ​ __________ mg/cm³ ​ What is the concentration to four decimal places of the drug in the organ after 30 sec? ​ __________mg/cm³ ​ What will be the concentration of the drug in the long run? ​ __________mg/cm³