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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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 2050 ( t = 4 )?
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 2050 ( t = 4 )? (Multiple Choice)
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(40)
(40) How long will it take an investment of $4,000 to double if the investment earns interest at the rate of 7% compounded continuously? Round your answer to the nearest hundredth. 
__________ year(s)
__________ year(s) (Short Answer)
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(32) Use logarithmic differentiation to find the derivative of the function. 
(Essay)
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(41) Use the facts that log 3 = 0.4771 to find the value of the logarithm. 
(Multiple Choice)
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(33) Find an equation of the tangent line to the graph of 
at its inflection point.
at its inflection point. (Essay)
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(30) 
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?
__________ What is the rate of change of the strain with respect to the load when the load is 400 kg?
__________ (Essay)
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(27) If the temperature is constant, then the atmospheric pressure P (in pounds/square inch) varies with the altitude above sea level h in accordance with the law 
, where 
is the atmospheric pressure at sea level and k is a constant.
If the atmospheric pressure is 15 
at sea level and 13.5 
at 5,000 ft, find the atmospheric pressure at an altitude of 15,000 ft.Please round the answer to one decimal place.
__________ 
How fast is the atmospheric pressure changing with respect to altitude at an altitude of 15,000 ft? Please round the answer to four decimal places.
__________ 
, where is the atmospheric pressure at sea level and k is a constant.
If the atmospheric pressure is 15 at sea level and 13.5 at 5,000 ft, find the atmospheric pressure at an altitude of 15,000 ft.Please round the answer to one decimal place.
__________ How fast is the atmospheric pressure changing with respect to altitude at an altitude of 15,000 ft? Please round the answer to four decimal places.
__________ (Essay)
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(32) Sketch the graphs of the given functions on the same axes. 
(Multiple Choice)
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(40) 
__________On the basis of data collected during an experiment, a biologist found that the growth of the fruit fly (Drosophila) with a limited food supply could be approximated by the exponential model 
where t denotes the number of days since the beginning of the experiment. How fast was the population changing on the 20th day?
where t denotes the number of days since the beginning of the experiment. How fast was the population changing on the 20th day? (Multiple Choice)
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