Chat with AIExam 5: Exponential and Logarithmic Functions
Exam 1: Preliminaries209 Questions
Exam 2: Functions, Limits and the Derivative271 Questions
Exam 3: Differentiation331 Questions
Exam 4: Applications of the Derivative183 Questions
Exam 5: Exponential and Logarithmic Functions278 Questions
Exam 6: Integration313 Questions
Exam 7: Additional Topics in Integration250 Questions
Exam 8: Calculus of Several Variables205 Questions
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Use the curve-sketching guideline, to sketch the graph of the function. 
(Multiple Choice)
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Strontium 90, a radioactive isotope of strontium, is present in the fallout resulting from nuclear explosions.It is especially hazardous to animal life, including humans, because, upon ingestion of contaminated food, it is absorbed into the bone structure.Its half-life is 27 years.If the amount of strontium 90 in a certain area is found to be four times the "safe" level, find how much time must elapse before an "acceptable level" is reached.
(Multiple Choice)
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= __________
at the point 
.
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 70-ft tree.Please round the answer to two decimal places. 
__________ years
where t is the age of the tree in years.Estimate the age of a 70-ft tree.Please round the answer to two decimal places. __________ years (Short Answer)
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Use logarithmic differentiation to find the derivative of the function. 
(Essay)
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(37) Find an equation of the tangent line to the graph of 
at the point 
.
at the point . (Multiple Choice)
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(37) Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of 16% / year.Round your answer to the nearest hundredth.
__________%
(Short Answer)
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= __________Find an equation of the tangent line to the graph of 
at its inflection point.
at its inflection point. (Multiple Choice)
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(28) 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 
is the standard reference intensity.
What is the magnitude of an earthquake that has intensity 10 millions times that of 
? 
__________
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.
Hint: Observe that 
and use logarithmic differentiation.Round your answer to the nearest integer.
__________ 
where I is the intensity of the earthquake being measured and is the standard reference intensity.
What is the magnitude of an earthquake that has intensity 10 millions times that of ? __________
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.
Hint: Observe that and use logarithmic differentiation.Round your answer to the nearest integer.
__________ (Essay)
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(34) Skeletal remains of the so-called "Pittsburgh Man", unearthed in Pennsylvania, had lost 86% of the carbon 14 they originally contained.Determine the approximate age of the bones.Round your answer to the nearest year.Hint: the decay constant k for carbon 14 is equal to 0.00012.
__________ years
(Short Answer)
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(40) Find the interest rate needed for an investment of $5,000 to grow to an amount of $7,000 in 4 year(s) if interest is compounded continuously.
(Multiple Choice)
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