Question
Are exponential equations the same as exponential functions?
I am writing a summary of this year's Pre-Calculus lessons and one of the topics on the outline is "Exponential Equations", but on the lesson Power Points on my teacher's website there is only one labeled "Exponential Functions", are they the same thing?
I am writing a summary of this year's Pre-Calculus lessons and one of the topics on the outline is "Exponential Equations", but on the lesson Power Points on my teacher's website there is only one labeled "Exponential Functions", are they the same thing?
Answers
An equation is not a function. However, the definition of a function is usually written as an equation, as in
f(x) = 2e^x - 7
But, that's really just a definition. An equation is usually something you have to solve for a particular value. For example, you might have to solve the equation
e^x - 7x = 12sin(2x)
if you want to find some particular values of x which make the equation true. The above equation must be solved numerically or graphically, as at
http://www.wolframalpha.com/input/?i=solve+e^x+-+7x+%3D+12sin%282x%29
f(x) = 2e^x - 7
But, that's really just a definition. An equation is usually something you have to solve for a particular value. For example, you might have to solve the equation
e^x - 7x = 12sin(2x)
if you want to find some particular values of x which make the equation true. The above equation must be solved numerically or graphically, as at
http://www.wolframalpha.com/input/?i=solve+e^x+-+7x+%3D+12sin%282x%29