Exp.Growth­Decay Word Prob Notes.notebook
January 04, 2017
Warm Up:
Match the equation with its graph without using any technology...
a)
b)
c)
d)
1) y = ­6*(1/2)(x+2)
2) y = 1/2*(3/4)x
3) y = ­6*2(x­5)
4) y = 3*(7/3)x
Oct 11­12:14 PM
Try this with your group members (use any method you can think of, but see if you can incorporate the idea of the exponential functions we've been graphing):
You just bought a Mickey Mantle rookie card for its current value of $1500. Historically, the value of cards like this one go up by 6% each year.
How much will this card be worth when you retire in 50 years?
Oct 11­2:51 PM
1
Exp.Growth­Decay Word Prob Notes.notebook
January 04, 2017
When a real­life quantity increases or decreases by a fixed percentage each year (or other time period), the amount (y) of the quantity after (t) years can be modeled by the equations:
y = a(1 + r)t (increase)
y = a(1 ­ r)t (decrease)
where a is the initial amount and the growth rate or rate of decay, r, is the percent increase or decrease expressed as a decimal. The (1+r) and (1­r) are known as the growth/decay factor.
Oct 11­1:21 PM
Let's try another:
The average car loses 19% of its value each year. Write an equation that models the value of a car that was worth $30,000 new and is t years old, then use that model (equation) to find the value of the car after 10 years.
Oct 11­2:42 PM
2
Exp.Growth­Decay Word Prob Notes.notebook
January 04, 2017
A common application for exponential functions is the idea of Compound Interest. Compound means that, as time goes by, interest will be paid or earned on the interest already accrued ­ not just the principal (as it was when you used to use the simple interest formula I = Prt).
Compound Interest formula:
r nt
A = P(1 + )
n
where A is the amount of money in the account, P is the principle (or starting amount), r is the annual interest rate (as a decimal), n is number of times per year the interest is compounded, and t is number of years.
Jan 4­1:26 PM
One more example: If you invest the $10,000 you saved for a used car in an account that pays 4.5% annual interest compounded monthly, and you don't touch that account for the next 45 years ­ How much will you be able to spend on a car when you retire in 45 years?
Jan 4­1:52 PM
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