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Exponential Functions

Exponential Functions 1.15 - Solution

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

Writing the Equation

To write the equation, we first need to define the variables. Let be the population, and let be the number of years after the initial value. In this case, the initial value is a population of Since the population decreases 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