$15,000 deposit that earns 10% annual interest compounded monthly. Do Now 1/23/19 Take out HW from last night. Text p. 319, #6-38 evens, 44-60 multiples of 4, & 63a Copy HW in your planner. Text p. 324, #1-19 all Quiz sections 6.1-6.4 Thursday In your notebook, write a function that represents the balance after t years. $15,000 deposit that earns 10% annual interest compounded monthly.

COMPOUND INTEREST the interest earned on the principal and on previously earned interest. P = Principal (initial investment) r = annual interest rate (as a decimal) t = time in years n = number of times interest is compounded per year

$15,000 deposit that earns 10% annual interest compounded monthly. Compound Interest Write a function that represents the balance after t years. $15,000 deposit that earns 10% annual interest compounded monthly.

Homework Text p. 319, #6-38 evens, 44-60 multiples of 4, & 63a &b

Homework Text p. 319, #6-38 evens, 44-60 multiples of 4, & 63a &b

Homework Text p. 319, #6-38 evens, 44-60 multiples of 4, & 63a &b

Homework Text p. 319, #6-38 evens, 44-60 multiples of 4, & 63a &b

Homework Text p. 319, #6-38 evens, 44-60 multiples of 4, & 63a &b

Learning Goal Learning Target SWBAT simplify, graph, and solve exponential expressions, equations, functions and sequences. Learning Target SWBAT identify and evaluate exponential growth and decay functions

“Exponent Rules” Notecard Create a “Exponents Rules” Notecard for your quiz tomorrow. Take the next 10 minutes to review the notes and create your notecard. You may use this notecard on the quiz. You may write on both sides, but must use the card given to you.

Section 6.1 “Properties of Exponents” (1) Product of Powers Property (2) Power of a Power Property (3) Power of a Product Property

(4) Quotient of Powers Property (5) Power of a Quotient Property

Scientific Notation A number is written in scientific notation if it has the form: where c is greater than or equal to 1 but less than 10. Standard form Product form Scientific notation **HINT: How many spots has the decimal point moved?

Section 6.2 “Radical and Rational Exponents” If bn = a then b is the nth root of a. radical index radicand Radical form Rational form

Rational Exponents A rational exponent does not have to be of the form 1/n. Other rational numbers can also be used as exponents.

Section 6.3 “Exponential Functions” -a nonlinear function of the form where a ≠ 0, b ≠ 1, and b > 0. y = abx As the independent variable ‘X’ changes by a constant amount, the dependent variable ‘Y’ is multiplied by a constant factor, which means consecutive Y values form a constant ratio.

Section 6.4 “Exponential Growth and Decay” -occurs when a quantity increases by the same factor over equal intervals of time. a > 0 and r > 0 rate of growth (in decimal form) final amount y = a(1 + r)t time initial amount growth factor

y = a(1 – r)t EXPONENTIAL DECAY- -occurs when a quantity decreases by the same factor over equal intervals of time. a > 0 and 0 < r < 1 rate of decay (in decimal form) final amount y = a(1 – r)t time initial amount decay factor

Using Exponential Functions Write a function representing the situation. Your salary of 20,000 increases by 4% a year. A population of 210,000 decreases by 14.5% a year. Exponential decay because the population is decreasing. Exponential growth because your salary is increasing.

Interpreting Exponential Functions Determine whether each function represents exponential growth or decay. Identify the rate of change. Exponential growth because b is greater than 1. Exponential decay because b is less than 1. To determine the percent rate of change use the growth factor (1 + r ) to find the rate of growth. To determine the percent rate of change use the decay factor (1 - r ) to find the rate of decay. Growth factor: 1 + r = 1.07 Decay factor: 1 - r = 0.88 r = 0.07 r = 0.12 Rate of change = 7% Rate of change = 12%

Rewriting Exponential Functions Rewrite each function to determine if it represents exponential growth or decay. Rewrite function so t is isolated. Rewrite function so t is isolated. Evaluate the power. Evaluate the power. Exponential decay because b is less than 1. Exponential growth because b is greater than 1.

COMPOUND INTEREST the interest earned on the principal and on previously earned interest. P = Principal (initial investment) r = annual interest rate (as a decimal) t = time in years n = number of times interest is compounded per year

BIG IDEAS ONLINE PRACTICE QUIZ

Homework Text p. 324, #1-19 all Quiz Thursday Sections 6.1-6.4