Exam 13: Exponential Functions and Logarithmic Functions

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Find an equation of the inverse of the relation. -y = Find an equation of the inverse of the relation. -y =   + 5x + 5x

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Using a calculator, find to the nearest ten-thousandth. -Using a calculator, find to the nearest ten-thousandth. -

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Solve the problem. -A size 4 dress in Country C is size 32 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 12). Find a formula for the inverse of the function described.

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Solve. -How long will it take for the population of a certain country to triple if its annual growth rate is 7.8%? Round to the nearest year. Use the exponential growth model Solve. -How long will it take for the population of a certain country to triple if its annual growth rate is 7.8%? Round to the nearest year. Use the exponential growth model

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Determine whether the function is one-to-one. -f(x) = Determine whether the function is one-to-one. -f(x) =

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Express in terms of logarithms of a single variable or a number. -Express in terms of logarithms of a single variable or a number. -

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Solve the equation. -Solve the equation. -  = 73 (Round to the nearest thousandth.) = 73 (Round to the nearest thousandth.)

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Find the requested composition of functions. -Given f(x) = -5x + 2 and g(x) = 2x + 4, find Find the requested composition of functions. -Given f(x) = -5x + 2 and g(x) = 2x + 4, find

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Solve. -The number of acres in a landfill is given by the function Solve. -The number of acres in a landfill is given by the function   where t is measured in years. How many acres will the landfill have after 4 years? (Round to the nearest acre.) where t is measured in years. How many acres will the landfill have after 4 years? (Round to the nearest acre.)

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Solve. -Solve. -  = x = x

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Simplify. -Simplify. -

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Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Without using a calculator, explain why Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Without using a calculator, explain why   must be greater than 8 but less than 16. must be greater than 8 but less than 16.

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Determine whether the given function is one-to-one. If so, find a formula for the inverse. -f(x) = Determine whether the given function is one-to-one. If so, find a formula for the inverse. -f(x) =

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Determine whether the function is one-to-one. -f(x) = Determine whether the function is one-to-one. -f(x) =   + x  + x

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Using a calculator, find to the nearest ten-thousandth. -ln 0.995

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Graph. -f(x) = Graph. -f(x) =    Graph. -f(x) =

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Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain how the equation log x = 1 could be solved using the graph of f(x) = log x.

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Graph. -x = 2y Graph. -x = 2y

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Solve the equation. -ln(5x - 1) = ln 3 - ln (x - 3)

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Solve for x. -Solve for x. -

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