1. Exponential Growth & Decay and Compound Interest

2. Growth: goes up in value, use this formula!
y = c(1+r)t 1+r>1
Decay: goes down in value, use this formula!
y = c(1- r)t 1- r <1

3. Identify the following as growth or decay
You are checking the part being raised to the power
-bigger than 1 is growth
-between 0 and 1 is decay
y = 500(1.20)5
y = 375(.078)t
y = 5(1.078)6
y = 30(.99)4

4. Example:
You buy a new 10 speed bike for $150. It loses value at a rate of 15% per year. What is it’s worth in 3 years?
Worth = cost(rate)years
w = c(1-0.15)3 (a loss means –15%)
w = 150(.85)3
w = 92.12
The bike was only worth $92.12 in 3 years.

5. Write a general equation for the following
You purchased a car for $35,000. The minute you drove it off the lot it started going down in value by 1.3%. Write an equation for its value in the future.
You just purchased a painting as an investment and it is suppose to appreciate it value at a rate of 3.65% each year. Write an equation for its value in the future.
f(t) = 35,000(0.987)t
f(t) = P(1.0365)t

6. Simple interest p(t)= p0 + p0 rt
(will be a linear function)
To find the amount of interest you earn use I=prt
To find the total amount you have use A=p+prt
p(t)= p0 + p0 rt
I = interest
A or p(t) = total amount you have
p or p0= principal amount you start with
r = rate of interest (write % as a decimal)
t= time in years

7. You have $3,150 after one year.
If you invest $3,000 at 5% for one year, how much will you make for the year?
I = prt
I = 3000  0.05  1
I = 150
You made $150 for the year.
p(1)= p + prt
p(1)=  0.05  1
p(1)= 3150
You have $3,150 after one year.

8. (will be an Exponential Function)
Compound Interest
(will be an Exponential Function)
Compound interest formula:
A = p(1+r)t
p(t) = p0(1+r)t
A or p(t) = total amount you have
p or p0= principal amount you start with
r = rate of interest (write % as a decimal)
t= time in years

9. Find the total amount in your account if you start with $750 at 7
Find the total amount in your account if you start with $750 at 7.5% interest compounded annually for 2.5 years.
A = p(1+r)t
= 750( )2.5 (Plug in what you know)
= 750(1.075)2.5 (simplify)
= $898.63

10. A = p(1+r)t (Plug in what you know) 200 = p(1.07)5 (then isolate p)
How much should you invest at 7% compounded annually to have $200 after 5 years?
A = p(1+r)t (Plug in what you know)
200 = p(1.07)5 (then isolate p)
200 = p (1.07)5
142.60= p

11. You put $100 in the bank at 4% interest compounded annually and leave it until you are 60. Write a function to show how much money will you have as a function of time in years and solve.
f(t) = p(1+r)t
f(46) = 100(1.04)46 (This assumes you are currently 14)
f(46) =
You will have $ when you are 60

12. What if you put the same $100 in a mutual fund that pays 10% interest compounded annually until you’re 60?
Write a function to show how much money will you have as a function of time in years and solve.
f(t) = p(1+r)t
f(46) = 100(1.10)46
f(46) =
You would have $8, when you are 60