What do you see?
Warm-up (Hint: not all answer will be used)
1. Which equations below model exponential growth?
2. Which equations model exponential decay?
A. y = 4x
B. y = 3(0.6)x
C. y = -5x
D. y = 3x
E. y = ½ (8x)
F. y=10x
G. y = 1x
H. y = 2.5(0.2)x
I. y = 3x2
A.
B.
E. F.
H.
Homework Answers
Homework Answers
Homework Answers
Homework Answers
Homework Answers
Homework Answers
Lesson 10-6A
Objective:
Solve problems involving exponential growth
General Growth Formula
y =
b = initial amount, starting amount
a = growth factor
x = time
b • a x
Example #1
The population of a certain strain of bacteria grows according to the formula y = b(2)x, where x is the time in hours. If there are now 50 bacteria, how many will there be in 2 days (48 hours)?
y = b • a x
y = 50• 248
y = 1.41 x 1016
≈ 14,100,000,000,000,000
Example #2
If the number of rabbits in a cage quadruples (x4) every year, how many will be in the cage after 6 years if you start out with 2?
y = b • a x
y = 2 • 4 6
y = 8,192
Percentage Growth Formula
y =
b = initial amount
r = % growth (as a decimal)
x = time
b (1 + )xr
Example #3
In 2004, the number of weekly passes sold by Tri-Cities Transit was 98,481 and was growing at a rate of 3.8% per year. At this rate, estimate the number of passes sold in 2007.
y = b(1 + r)x
y = 98481(1 + ).038 3
y = 98481(1.038)3
y = 110,139
Example #4
In 2001, the population of Lagos, Nigeria was about 7,998,000. Use the population growth of 4.06% per year to estimate the population in 2009?
y = b(1 + r)x
y = 7998000 (1 + ).04068
y = 7998000(1.0406)8
y = 10,996,436
Compound Interest Formula
A =
P = Principal (what you invest)
r = interest rate (as a decimal)
n = number of times interest is
compounded per year
t = years
P (1 + )nr
n t
• Quarterly: n= 4
• Semi-annually: n=2
• Monthly: n=12
Example #5
If you invest $500 compounded monthly for 10 years at an interest rate of 6%, what will your total investment be worth?
P(1 + )nr
n t
A =
500(1 + )12.06
12 (10)
A =
A = 500(1.005)120
A = $909.70
Example #6
Determine the amount of an investment if $1000 is invested at an interest rate of 4% compounded semi-annually for 5 years.
P(1 + )nr
n t
A =
1000(1 + )2.04
2 (5)
A =
A = 1000(1.02)10
A = $1218.99
Assignment: 10-6 A
p. 563 #9-13, 14, 15, 18, 21
Quiz (10-5 and 10-6) on Friday!