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## 1.3

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**1.3**Exponential Functions**What you’ll learn about…**• Exponential Growth • Exponential Decay • Applications • The Number e …and why Exponential functions model many growth patterns.**Exponential Growth**If 0 < a < 1, then the graph of f looks like the graph of y = 2-x = .5x.**Compound Interest**The formula for calculating the value of an investment that is awarded annual compound interest is T=P(1+r)twhere T is the total value of the investment, P is the principal, r is the rate of interest (as a decimal) and t is the number of years.**Calculate the value of a 3 year certificate of deposit given**the initial investment was $500 and the CD earns 2% annually.**If an investment earns 4% annually, how long will it take**for the value of the investment to double?**Half-life**Exponential functions can also model phenomena that produce decrease over time, such as happens with radioactive decay. The half-life of a radioactive substance is the amount of time it takes for half of the substance to change from its original radioactive state to a non-radioactive state by emitting energy in the form of radiation.**Exponential Growth and Exponential Decay**The function y = k ● ax, k > 0, is a model for exponential growth if a > 1, and a model for exponential decay if 0 < a < 1.**Example Exponential Functions**Use a graphing calculator to find the zero’s of f(x)= 4x – 3.**The Number e**The exponential functions y = exand y = e-x are frequently used to model exponential growth or decay. Interest compounded continuously uses the model y = P ert, where P is the initial investment, r is the interest rate (as a decimal) and t is the time in years.**Example The Number e**• The approximate number of fruit fies in an experimental population after t hours is given by Q(t) = 20e0.03t, t ≥ 0. • Determine the initial number of flies in the poplation. • How large is the population after 72 hours? • Graph the function. [0,100] by [0,120] in 10’s**Quick Quiz Sections 1.1 – 1.3**3. The half-life of a certain radio active element is 8 hours. There are 5 grams present initially. Which of the following gives the best approximation when there will be 1 gram remaining? • 2 • 10 • 15 • 16 • 19**Assignment**pages 26 – 28, 3-21 multiples of 3, 23-27, 32, 36, 40