Exponential Growth And DecayPresentation Transcript
Exponential Growth and Decay
An exponential function can either be increasing or decreasing. INCREASING – from small to big Example: 1, 2, 3, 4, 5, 6, 7, 8, … DECREASING – from big to small Example: 10, 9, 8, 7, 6, 5, 4, …
EXPONENTIAL GROWTH – an increasing exponential function. EXPONENTIAL DECAY – a decreasing exponential function.
RECALL An exponential function is a function of the form 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. If b > 1, the exponential function is an increasing exponential function. If b < 1, the exponential function is a decreasing exponential function.
Exponential Growth Exponential growth can be modeled with the function y = a ∙ bxfor a > 0 and b > 1. starting amount (when x = 0) y = a ∙ bx exponent Thebase, which is greaterthan 1,is the growth factor.
Exponential Decay The function y = a∙bxmodels exponential decay for a > 0 and 0 < b < 1. starting amount (when x = 0) y = a ∙ bx exponent Thebase, which is between 0 and 1,is the decay factor.
Determine whether the following functions model EXPONENTIAL GROWTH or EXPONENTIAL DECAY. exponential growth exponential decay exponential growth exponential decay
Problem Solving 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?