What do you remember about the following 1

What do you remember about the following: 1) What is factoring? Give an example. 2) What exponent rules do you remember? Give examples (there are 5). REMINDERS: Sign up for Remind. com The code is on the class web site. Check out tutoring times on web site, remind texts, front white board, outside the door.

6. 1 Notes: Growth and Decay Functions

What is an exponential growth function? The variable is in the exponent rather than the base. Exponential growth increases slowly at first, then drastically increases as time continues. The basic graph looks like:

Basic Graph info: Equation: With f(x) = bx , where b > 1 a “go-to” point (always passes through) at (0, 1) Horizontal asymptote at y = 0. Wait…what’s an “asymptote? ”……. it’s a line that the graph will never cross, only approach forever. How We do we evaluate an exponential growth function? pick some values for “x” and plug them in

Exponential Decay What is an exponential decay function? There is a rapid decrease initially and then the decrease becomes more gradual. Equation: f(x) = bx , where 0 < b < 1 (basically, they are fractions). The basic graph has the same go – to point at (0, 1) and asymptote at y = 0. The base is between 0 and 1. The graph looks like:

Graphing: Pick at least 3 values for x, plug them in to find y. Graph the points EX x A: y = 2 x f(x) B: y = 3 x x f(x)

Evaluating exponential decay functions: EX x A: f(x) = (½)x f(x) B: y = x f(x)

Solving Real-world problems:

Solving Real-world problems:

HW: p. 300 #3 – 24

Warm Up:

Exponential Models: Exponential growth model: y = a(1 + r)t y = amount after increase a = initial amount r = percent increase written as a decimal t = # of years EX: y = 25, 000(1 + 0. 13)5 EX: In 2000, the world population was about 6. 09 billion. During the next 13 years, the world population increased by about 1. 18% each year. Write an exponential growth model giving the population y (in billions) t years after 2000. Estimate the population in 2005.

Exponential Models: Exponential decay model: y = a(1 - r)t y = amount after decrease a = initial amount r = percent decrease written as a decimal t = # of years Example: y = 15, 500(1 – 0. 17)7 Example: You purchased the new BMW 3 Series car for $35, 357. The car depreciates at a rate of 13 percent per year. Write an equation to model the drop in value of the car, then determine the value of the car in 6 years.

Compund Interest: Interest is the money earned on an investment. This could be a bank account, certificate of deposit, stocks, bonds, loan to someone, etc. Depreciation is the money lost over time on something purchased. The most thorough of example for this is a car. Interest: Interest can be compounded (calculated) once a year, twice a year, three times a year, etc, up to continuously. We will use the compound interest formula:

If we compound: year): we calculate interest (per Quarterly 4 times Monthly 12 times Bi-monthly 24 times Weekly 52 times Daily 365 times EX: You deposit $4000 in an account that pays 2. 92% annual interest. Find the balance after 1 year if the interest is compounded a) quarterly and b) daily.

DUE in class: p. 315 #37 - 44

Warm Up