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Exponential Functions

Exponential Functions 1.10 - Solution

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First, we write an exponential function to model the given situation, thus, recall its general form. In this formula, is the initial value and where is the rate of change. If the function represents growth then Conversely, if it represents decay, then

Writing the Equation

To write the equation, we first need to define the variables. Let be the population, and the number of years after that have passed. In this case, the initial value is a population of Since the population increases each year, we have that

Finding the Amount After the Specified Time

Now, we want to find the population after years. To do so, we will substitute for in our model equation.
We found that, after years, the population will be approximately