TODAY IN ALGEBRA 2.0…

WARM UP: Write and solve equations using exponential GROWTH

Learning Target 1: 7.2 You will write and solve equations using exponential DECAY

Independent Practice

WARM UP: EXPONENTIAL GROWTH 1. a. The projected worth (in millions of dollars) of a large company is modeled by the equation . The variable t represents the number of years since 1999. What is the projected annual percent of growth?

b. What is the company worth in 2014?

2. If $1200 was deposited into an account that pays 9% annual interest compounded monthly, how much will the account have after 5 years?

7.2 EXPONENTIAL GROWTH and DECAY COMPARISON

PARENT EQUATION: 𝑦=𝑎𝑏𝑥

𝑎=1𝑏>1 𝑎=10<𝑏<1

7.2 EXPONENTIAL DECAY

EXPONENTIAL DECAY MODEL:

EXAMPLE: A new snowmobile costs $4200. The value of the snowmobile decreases by 10% each year. Write an exponential decay model giving the snowmobile’s value after (t) years. Estimate the value after 3 years.

𝑦=𝑎(1−𝑟 )𝑡

7.2 EXPONENTIAL DECAY: PRACTICEThe value of a snowmobile has been decreasing by 7% each year since it was new. If the snowmobile was bought for $5200, what would the value be in 3 years?

7.2 EXPONENTIAL DECAY: EXAMPLEThe number of acres of Ponderosa pine forests decreased in the western United States from 1963 to 2002 by 0.5% annually. In 1963 there was about 41 million acres of Ponderosa pine forests.

a. Write a function that models the number of acres of Ponderosa pine forests over time t.

b. To the nearest tenth, about how many million acres of Ponderosa pine forests were there in 2002?

7.2 EXPONENTIAL DECAY: PRACTICEYou buy a new personal computer for $1600. It is estimated that the computer’s value will decrease by 50% each year.

a. Write a function that models the value of your computer over time t.

b. About how much would your computer be worth in 4 years?

7.2 EXPONENTIAL DECAY: EXAMPLEIn the exponential decay model , identify the initial amount, the decay factor, and the percent decrease.

7.2 EXPONENTIAL DECAY: PRACTICEIn the exponential decay model , identify the initial amount, the decay factor, and the percent decrease.

HOMEWORK #2:

Pg. 489: 1, 26, 30, 31, 33

If finished, work on other assignments:

HW #1: Pg. 483: 28-30, 37, 38 Pg. 543: 27, 28