Exponential Growth And Decay

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Exponential Growth And Decay

  1. 1. Exponential Growth and Decay<br />
  2. 2. An exponential function can either be increasing or decreasing.<br />INCREASING – from small to big<br />Example: 1, 2, 3, 4, 5, 6, 7, 8, …<br />DECREASING – from big to small<br />Example: 10, 9, 8, 7, 6, 5, 4, …<br />
  3. 3. EXPONENTIAL GROWTH – an increasing exponential function.<br />EXPONENTIAL DECAY – a decreasing exponential function.<br />
  4. 4. RECALL<br /> An exponential function is a function of the form <br />f(x) = a ∙ bxwhere a is a nonzero constant, b is greater than 0 and not equal to 1 and x is any real number.<br />If b &gt; 1, the exponential function is an increasing exponential function.<br />If b &lt; 1, the exponential function is a decreasing exponential function.<br />
  5. 5. Exponential Growth<br />Exponential growth can be modeled with the function <br />y = a ∙ bxfor a &gt; 0 and b &gt; 1.<br />starting amount (when x = 0)<br />y = a ∙ bx<br />exponent<br />Thebase, which is greaterthan 1,is the growth factor.<br />
  6. 6. Exponential Decay<br />The function y = a∙bxmodels exponential decay for <br />a &gt; 0 and 0 &lt; b &lt; 1.<br />starting amount (when x = 0)<br />y = a ∙ bx<br />exponent<br />Thebase, which is between 0 and 1,is the decay factor.<br />
  7. 7. Determine whether the following functions model EXPONENTIAL GROWTH or EXPONENTIAL DECAY.<br />exponential growth<br />exponential decay<br />exponential growth<br />exponential decay<br />
  8. 8. Problem Solving<br />In 1990, Bangkok’s population was about 13 million. If the city’s population has grown about 1.7 % each year, what is the population of Bangkok in year 1995?<br />

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