# MDC MAC 2233 - Exponential Functions (2 pages)

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## Exponential Functions

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## Exponential Functions

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MAC2233 3 4 North FIU MDC 4 1 Exponential Functions Exponential Function f x bx b 0 b 1 for every real number x For b 1 f x is constantly increasing lim f x 0 and lim f x x x For 0 b 1 f x is constantly f x and lim f x 0 See your book for a review of definitions and basic decreasing xlim x properties of exponents Compound Interest If P dollars are invested at an annual interest rate r expressed as a decimal and interest is compounded k times a year the future value kt r balance B t after t years will be B P 1 if it is compounded continuously the balance will k be B Pe rt In order to have a given balance B in t years invested an annual rate r compounded kt r 1 if it is k times a year the Principal P invested now present value is given by P B k compounded continuously the principle is given by P Be a e5 1 Evaluate b e 1 kt c 3 x 1 2 Sketch the curves on the same graph y 3 and y 3 x Evaluate the following 3 5 27 2 3 8 Simplify 4 3 3 1 2 4 x 2 3 y 2 x 3 4 z 4 1 6 2 16 4 125 3 81 8 1 4 e MAC2233 3 4 North FIU MDC Solve for x 3x 6 1 4 8 2 x 7 32 x 3 92 x 8 Suppose that 5000 is invested at annual interest rate of 5 compounded daily What will the balance be in 40 years How much would the balance be if it were compounded continuously 9 If parents estimate that it will take 100 000 to send their child to college in 18 years how much should they invest now in a portfolio that is expected to yield an average of 9 5 a year compounded monthly 10 The gross domestic product GDP of a certain country was 500 billion at the beginning of 2000 and increases at the rate of 2 7 per year a Express the GDP of this country as a function of the number of years t after 2000 b What does this formula predict the GDP will be at the beginning of the year 2010

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