4.1 Exponential FunctionsMAC2233 (3.4) FIU, MDC-North4.1 Exponential FunctionsExponential Function: f(x) = bx (b > 0, b ≠ 1) for every real number x. For b > 1, f(x) isconstantly increasing, x xf x and f xlim ( ) 0, lim ( )�- � ��= =+�. For 0 < b < 1, f(x) is constantlydecreasing, x xf x and f xlim ( ) , lim ( ) 0�- � ��=+� =. [See your book for a review of definitions and basicproperties of exponents.]. Compound Interest: If P dollars are invested at an annual interestrate r (expressed as a decimal) and interest is compounded k times a year, the future value(balance) B(t) after t years will be ktrB Pk1� �= +� �� �; if it is compounded continuously, the balance willbe rtB Pe=. In order to have a given balance B in t years invested an annual rate r compoundedk times a year, the Principal P invested now (present value) is given by ktrP Bk1-� �= +� �� �; if it iscompounded continuously, the principle is given by ktP Be-=. 1. Evaluate: [a] e5[b]e13-[c]e412. Sketch the curves on the same graph: y = 3x and xy13� �=� �� �Evaluate the following:3.( )32 423 327 8-+4.1 24 316 12581 8-� � � �� � � �� � � �5. Simplify:( ) ( )x y xz162 323 44---� �� �� �� �� �MAC2233 (3.4) FIU, MDC-NorthSolve for x:6.xx314 82� �=� �� �7.x x2 3 23 9- -= 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
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