what do you see?. warm-up (hint: not all answer will be used) 1.which equations below model...

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!