07.04 Notes.docx

# Exponential equations are great if you are looking to

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decay has occurred. Exponential equations are great if you are looking to solve for the amount after the growth or decay. If the situation asks you to solve for the time needed to reach a given amount, consider using logarithms. It is possible to replace the A using function notation. P The P represents the principle which is the same as the amount at the very beginning. Examples of principles are the money you put into an account, the population of bacteria before it starts growing, or the amount of an isotope before it starts decaying. 1 + r This part has a big effect on the equation. The r represents the rate of change . So, if a loan is going to increase by 3%, then the r = 0.03. However, if the loan decreases 3%, then r = −0.03. If 1 + r is greater than 1, then the exponential equation is a growth equation. If 1 + r is less than 1, then it is a decay equation. If 1 + r = 1, then the r = 0 and it is a linear equation! t The t represents the amount of times the growth has occurred. If a fly population doubles every year and you want the population after 10 years, then t = 10. It is important to make sure your units match.
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