Warm-Up

• In 2010, Mr. Stewart bought a copy of “The Lion King” VHS signed by the entire cast for $45. The selling price of the VHS increases 6.7% per year. How much would the VHS sell for if Mr. Stewart sold it in 2025?

Homework Solutions1. Ask for graph

1. y-intercept : (0,1)2. Asymptote : y =2

2. Ask for graph1. y-intercept : (0,7.4)2. Asymptote : y =0

3. Ask for graph1. y-intercept : (0,1)2. Asymptote : y =0

7. ≈ 20.0868. ≈ 0.5139. ≈ 5.47410. ≈ -0.19911. ≈ 0.01512. ≈ 12.266

Modeling Exponential Situations

• We have been modeling exponential situations since introducing the lesson!!!!

• When you’re modeling exponential situations, you’re given a real world situation in which you will need to set up an equation and solve for the final amount given a certain time

Exponential growth/decay

• >1, the function models an exponential growth. • and 0<<1, the function models an exponential decay. • Remember represents your growth or decay factor.• You can use actual year if exponent is t, you just have to

do t-initial year.

Example 1:

• The population of the popular town of Smithville in 2003 was estimated to be 35,000 people with an annual rate of increase of about 2.4%.• Will this function model growth or decay?• What is the growth factor?• Write an equation to model future growth• Use your equation to estimate the population in 2007 to the

nearest hundred people.

You try 1:

• Matt bought a new car at a cost of $25,000. The car depreciates approximately 15% of its value each year.• Will this function model growth or decay?• What is the decay factor?• Write an equation to model the decay value of this car.• What will the car be worth in 10 years?

Compound Interest

• Compounded more than once a year

• n: how many times per year interest is compounded• t: time in years• r: interest rate• P: Principal ( initial amount)

Explanation of n

• When n is described as one of the following, this is the numeric value you enter:

Monthly Quarterly

Annually Daily Semi-annually

Bi-annually

12 4 1 365 2 1/2

Example 2: • Your first credit card charges 12.49% to its customers and compounds interests monthly.

Within one day of getting your credit card, you max out the credit limit by spending $1,200.00. If you do not buy anything else on the card and you do not make any payments, how much would you owe the company after:

• a). 1 year:  • b). 10 years:  • c). 6 months:

You try 2:

• Jose invests $500 at a bank offering 10% interest compounded quarterly. Find the amount of the investment at the end of 5 years (if untouched).

• Extension: What if the investment was compounded daily?

Compounded Continuously

• What does it mean when something is happening continuously?• e: natural base• P: Principal ( initial amount)• r: interest rate• t: time in years

Let’s Try:

• Tamika invests $600 at a bank offering 12% interests compounded continuously. Find the amount of the investment at the end of 7 years (if untouched).

Homework

Worksheet #25