Algebra II BC - Tredyffrin/Easttown School District



Alg 2 BC U8 Day 3 – Properties of Exponential Functions, “e”, Continuously Compounded Interest

Review: A concord jet is flying at a speed of 1300 mph when the engine dies. Four seconds later, the plane has

slowed down to 852.93 mph as it drifts in for an emergency landing. If the speed of the plane is decreasing

exponentially:

a) Write the particular equation y = abx, expressing speed in terms of time.

b) Predict the plane’s speed after 25 seconds (to the nearest mile per hour).

c) Why is this model not reasonable for large values of time?

d) At what time will the plane’s speed be 500 mph? (For this one, use your calculator and the “CALC” intersect concept.)

Warm-up, just for fun (…or maybe not …)

Given the function [pic] , fill in the xy-chart below. Round to 7 places past the decimal:

x y x y

1 50

2 100

5 10,000

10 1,000,000

25 1,000,000,000

Suppose Bob invests $2000 at an annual interest rate of 4.5%. How much will you have after 5 years?

Interest Compounded Annually:

Interest Compounded Quarterly

Interest Compounded Monthly:

Bob (from a previous word problem) enjoys the fact that he can get “compound interest”, earning interest on the interest. He realizes that the more often the interest is compounded, the more money he makes. So, he starts looking for a bank that will compound his interest as often as possible. He comes across an incredible deal, in which he earns an annual interest rate of 100% on his money, and the interest will be compounded DAILY!

For each $1 in his account, how much will he have at the end of the year? (Assume a NON-leap year.)

How much MORE is that than if the interest had only been compounded ANNUALLY?

Suddenly, the bank decides to compound the money HOURLY! Now how much does he have at the end of the year?

And finally, they compound the money EVERY SECOND! Now, how much does he have at the end of the year?

** Do you noticed anything about the numbers you are getting? **

Introducing ……. e = 2.71828182846……..= [pic]

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Compound Interest Formula:

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