Exam_2_Solns precalc

# Exam_2_Solns precalc - MATH 105 SECOND MIDTERM EXAM NAME...

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2 1. (3 points each) Circle “True” if the statement is true and “False” if the statement is false. Then state the exact range of each function. (a) If the domain of f ( x ) = e x is taken to be −∞ < x < , then f is an invertible function. True False Range: 0 < y < (b) If the domain of f ( x ) = e x is taken to be 0 < x < , then f is an invertible function. True False Range: 1 < y < (c) If the domain of f ( x ) = ln( x ) is taken to be 0 < x < , then f is an invertible function. True False Range: −∞ < y < (d) If the domain of f ( x ) = ln ( e x ) is taken to be −∞ < x < , then f is an invertible function. True False Range: −∞ < y < 2. (6 points) A scientist discovers a dinosaur fossil which contains a certain amount of the radioac- tive isotope carbon-14. The amount of carbon-14, in micrograms, in the fossil can be modeled by c = 200 e kt , where t is the age of the fossil in thousands of years. (a) What was the original amount of carbon-14 in the fossil? 200 micrograms (b) What is the sign of k in the model? Why? negative, to give exponential decay. (c) If t = f ( c ) is the age of the fossil as a function of how many micrograms c of carbon-14 it currently contains, what type of function is f ( c )? Explain your answer. f ( c ) is a logarithmic function. Notice that the function c = f - 1 ( t ) is the amount of carbon as a function of time, which is an exponential function. An inverse of an exponential function is a logarithmic function.
3 3. (8 points) For each graph, state the letter of the equation which best represents it.

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