GPS: MM3A2e, MM3A2f, MM3A2d

 MM3A2e – Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.  MM3A2f – Graph functions as transformations of f(x) = a x, f(x) = log a x, f(x) = ex, f(x) = ln x.  MM3A2g - Explore real phenomena related to exponential and logarithmic functions including half- life and doubling time.  MM3A3d –Solve a variety of types of equations by appropriate means, choosing among mental calculation, pencil and paper, or appropriate technology.

 The number denoted by the letter e is called the natural base e.  It is an irrational number defined as follows: As n approaches +∞, (1 + ) n approaches e≈  A function of the form f(x)=ae rx is called a natural base exponential function.  Continuously Compounded Interest – When interest is compounded continuously, the amount A in an account after t years is given by the formula A=Pe rt, where P is the principal and r is the annual interest rate expressed as a decimal.

PropertyStatement of Property Product of Power Property Power of a Power Property Power of a Product Property Negative Exponent Property Zero Exponent Property Quotient of Powers Property Power of a Quotient Property

 Simplify the expression ◦ e 6 * e 4 = e 6+4 = e 10 ◦ (-2e x ) 3 = (-2) 3 (e x ) 3 = -8e 3x ◦ 1

 Graph  Steps: ◦ Make a table ◦ Plot your points ◦ Asymptote? ◦ Domain & Range X-2012 Y

 Graph  Steps: ◦ Make a table ◦ Plot your points ◦ Asymptote? ◦ Domain & Range X-2012 Y

 Graph  Steps: ◦ Make a table ◦ Plot your points ◦ Asymptote? ◦ Domain & Range X-2012 Y

 You deposit $500 in an account that pays 3% annual interest compounded continuously. What is the balance after 2 years?  Use the formula for continuously compounded interest.  A = Pe rt

 Try page 141: 1-8

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