5.3 Applications of Exponential Functions

5.3 Applications of Exponential Functions - Applications of...

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Unformatted text preview: Applications of Exponential Functions Functions Section 5.3 Compound Interest Compound If If P dollars is invested at interest rate r (expressed as a decimal) per time period t, then A is the amount after t periods. A = P (1 + r ) t Continuous Compounding Continuous If If P dollars is invested at an annual interest rate of r, compounded continuously, then A is compounded the amount after t years. years. A = Pe rt Exponential Growth Exponential Exponential growth can be described by a function Exponential of the form x f ( x) = Pa Where f(x) is the quantity at time x, P is the initial f(x) quantity when x = 0 and a >1 is the factor by which the quantity changes when x increases by 1. If the quantity f(x) is growing at rate r per time If f(x) period, then a = 1 + r and f ( x) = Pa = P (1 + r ) x x Exponential Decay Exponential Exponential decay can be described by a function of Exponential the form x f ( x) = Pa Where f(x) is the quantity at time x, P is the initial f(x) quantity when x = 0 and 0 < a < 1 is the factor by which the quantity changes when x increases by 1. If the quantity f(x) is decaying at rate r per time 1. f(x) period, then a = 1 - r and f ( x) = Pa = P (1 − r ) x x Radioactive Decay Radioactive The amount of a radioactive substance that remains is given by the function remains f ( x) = P (0.5) x h Where P is the initial amount of the substance, x = 0 corresponds to the time when the radioactive decay began and h is the half-life of the half-life substance. substance. Joke Time Joke What What has wings and solves number problems? number A mothematician What What did one math book say to the other math book? to Don’t Don’t bother me! I’ve got my own problems! own ...
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