Exam 5: Exponential and Logarithmic Functions

Find the derivative of the function. ​ ​

Find the derivative of the function. ​

Use logarithms to solve the equation for t. Round your answer to four decimal places. ​ ​

Sketch the graphs of the given functions on the same axes. ​ and ​

Find the derivative of the function. ​ ​

Use logarithms to solve the equation for t. ​ ​

Find an equation of the tangent line to the graph of at the point . ​

Solve the equation for . ​

Wood deposits recovered from an archeological site contain 24% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Hint: the decay constant k for carbon 14 is equal to 0.00012.

Find the derivative of the function. ​

Find the present value of $70,000 due in 4 year(s) at the given rate of interest. Round your answers to the nearest dollar. ​ 4% / year compounded monthly ​ $__________ ​ 9% / year compounded daily ​ $__________

Find the derivative of the function. ​

The length (in centimeters) of a typical Pacific halibut t years old is approximately . What is the length of a typical 6-year-old Pacific halibut? How fast is the length of a typical 6-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain? Round your answers to the nearest tenth. length of a typical halibut = __________ cm halibut increasing = __________ cm/yr maximum length = __________ cm

Find the derivative of the function. ​ ​

During a flu epidemic, the number of children in the Woodbridge Community School System who contracted influenza after t days was given by . ​ How many children were stricken by the flu after the first day? Round your answer to the nearest integer. ​ __________ children ​ How many children had the flu after 10 days? Round your answer to the nearest integer. ​ __________ children ​ How many children eventually contracted the disease? Round your answer to the nearest integer. ​ __________ children

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

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. ​ What is the magnitude of an earthquake that has intensity 10 millions times that of I₀? ​ R = __________ ​ 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. ​

Evaluate the expression. ​ ​

Find the derivative of the function. ​

For children between the ages of 5 and 13 years old, the Ehrenberg equation gives the relationship between the weight W (in kilograms) and the height h (in meters) of a child. Use differentials to estimate the change in the weight of a child who grows from 1.1 m to 1.3 m. Round the answer to the nearest tenth. ​ __________ kg