The document discusses exponential growth and decay functions. Exponential growth functions have a base greater than 1, modeling an increasing pattern from small to big numbers over time. Exponential decay functions have a base between 0 and 1, modeling a decreasing pattern from big to small numbers. Examples are provided of functions modeling exponential growth and decay, along with explanations of how to determine which type of function based on the base.

1. Exponential Growth and Decay

2. An exponential function can either be increasing or decreasing.INCREASING – from small to bigExample: 1, 2, 3, 4, 5, 6, 7, 8, …DECREASING – from big to smallExample: 10, 9, 8, 7, 6, 5, 4, …

3. EXPONENTIAL GROWTH – an increasing exponential function.EXPONENTIAL DECAY – a decreasing exponential function.

4. 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.

5. Exponential GrowthExponential growth can be modeled with the function y = a ∙ bxfor a > 0 and b > 1.starting amount (when x = 0)y = a ∙ bxexponentThebase, which is greaterthan 1,is the growth factor.

6. Exponential DecayThe function y = a∙bxmodels exponential decay for a > 0 and 0 < b < 1.starting amount (when x = 0)y = a ∙ bxexponentThebase, which is between 0 and 1,is the decay factor.

7. Determine whether the following functions model EXPONENTIAL GROWTH or EXPONENTIAL DECAY.exponential growthexponential decayexponential growthexponential decay

8. Problem SolvingIn 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?