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  1. AP Pre Calculus
FlashcardFlashcardStudy GuideStudy GuideQuestion BankQuestion Bank

Exponential and Logarithmic Functions

Question 1
1 mark
college-boardPre-CalculusAPExam Style
1 mark

If the half-life of a radioactive substance is 7 years, expressed as an inverse exponential function, what is the initial quantity of the substance if after 14 years there are 5 grams remaining?

Question 2
1 mark
college-boardPre-CalculusAPExam Style
1 mark

What must hold true for both an exponential function bxb^xbx and its inverse logโกb(y)\log_b(y)logbโ€‹(y) related to their continuity properties?

Question 3
1 mark
college-boardPre-CalculusAPExam Style
1 mark

For which value does h(t)h(t)h(t), where h(t)h(t)h(t) is defined as h(t)=logโก9(t2โˆ’6t+14)h(t) = \log_9(t^2 - 6t + 14)h(t)=log9โ€‹(t2โˆ’6t+14), have an asymptote?

Question 4
1 mark
college-boardPre-CalculusAPExam Style
1 mark

Which equation represents the horizontal stretch by a factor of two for the exponential function g(x)=5โˆ’0.5xg(x)=5^{-0.5x}g(x)=5โˆ’0.5x?

Question 5
1 mark
college-boardPre-CalculusAPExam Style
1 mark

Which property do both the exponential function and its inverse share?

Question 6
1 mark
college-boardPre-CalculusAPExam Style
1 mark

If f(x)=axf(x) = a^{x}f(x)=ax, what is the base 'a' in the inverse function fโˆ’1(x)=logโกa(x)f^{-1}(x) = \log_{a}(x)fโˆ’1(x)=logaโ€‹(x)?

Question 7
1 mark
college-boardPre-CalculusAPExam Style
1 mark

What happens algebraically to find g(y), if you have h(x) such that h(x)=ae^(bx+c)+d and want g(y) which represents h's antilogarithm/inverse?

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Question 8
1 mark
college-boardPre-CalculusAPExam Style
1 mark

If there is an asymptote at y=0y = 0y=0 for the function g(x)=lnโก(x)g(x) = \ln(x)g(x)=ln(x), what conclusion can be drawn regarding the slope of the graph of function gโˆ’1(x)g^{-1}(x)gโˆ’1(x) as the input approaches infinity?

Question 9
1 mark
college-boardPre-CalculusAPExam Style
1 mark

What property must be true for an exponential function to have an inverse?

Question 10
1 mark
college-boardPre-CalculusAPExam Style
1 mark

How many years will it take for an investment to quadruple in value if it grows according to an exponential function with an inverse doubling time of six years?