University:
High School
Course:
High School Algebra
Academic year:

2020
Views:

61

Pages:

3
Author:

Omezzollifm

Exponential and Logarithmic Functions 6.1 Exponential Growth and Decay Functions Vocabulary: A(n) ______________________ function has the form 𝑦 = 𝑎𝑏 ! , where 𝑎 ≠ 0 and the base b is a positive real number other than 1. If 𝑎 > 0 and 𝑏 > 1, then 𝑦 = 𝑎𝑏 ! is an exponential _______________ function, and b is called the _______________ factor. If 𝑎 > 0 and 0 < 𝑏 < 1, then 𝑦 = 𝑎𝑏 ! is an exponential _______________ function, and b is called the _______________ factor. A(n) ______________________ is a line that a graph approaches more and more closely. Exponential Growth Model: Exponential Decay Model: Example 1: You take a 325 milligram (mg) dosage of ibuprofen. During each subsequent hour, the amount of medication in your bloodstream decreases by about 29% each hour. A. Write an exponential decay model giving the amount y (in mg) of ibuprofen in your bloodstream t hours after initial dose. B. Estimate how long it takes for you to have 100 mg of ibuprofen in your bloodstream. Example 2: Rewrite the function in the form 𝑦 = 𝑎(1 + 𝑟)" or 𝑦 = 𝑎(1 − 𝑟)" ; state the growth or decay rate. 𝑦 = 𝑎(0.25)"/$ Compound Interest: Consider an initial principal P deposited in an account that pays interest at an annual rate r (expressed as a decimal), compounded n times per year (if the account is compounded % monthly then n=12). The amount A in the account after t years is given by: 𝐴 = 𝑃(1 + &)&" Example 3: You deposit $9000 in an account that pays 1.46% annual interest. Find the balance after 3 years when the interest is compounded quarterly. The Natural Base Natural Base Functions A function of the form y = aerx is called a natural base exponential function. The number “e” is just a mathematical constant, approximately equal to 2.71828. This number is also known as Euler’s constant. Leonard Euler was the man who discovered it. You have a button on your calculator that has 𝑒 ! on it. If you plug in 𝑒 " you will get 2.71828. The graphs of the basic functions y = e x and y = e- x are shown. In Exercises 1–4, simplify the expression. 1. e- 9 • e12 2. 25e2 35e7 3. (2e-3x ) 5 • 2e x +1 4. 4 16e 24 x In Exercises 5–6, describe the transformation of f represented by g. Then graph each function. 5. 𝑓(𝑥) = 3! , 𝑔(𝑥) = 3! − 2 6. 𝑓(𝑥) = 𝑒 ! , 𝑔(𝑥) = 𝑒𝑥−3