Exponential Growth and Decay

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# Exponential Growth and Decay - PowerPoint PPT Presentation

Exponential Growth and Decay. Modified from the presentation at: www.mathisnothard.com/pages/.../ powerpoint s/exp growthdecay . ppt. E XPONENTIAL G ROWTH M ODEL. W RITING E XPONENTIAL G ROWTH M ODELS. C is the initial amount. t is the time period. y = C (1 + r ) t.

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### Exponential Growth and Decay

Modified from the presentation at: www.mathisnothard.com/pages/.../powerpoints/expgrowthdecay.ppt

EXPONENTIAL GROWTH MODEL

WRITING EXPONENTIAL GROWTH MODELS

C is the initial amount.

t is the time period.

y = C (1 + r)t

(1 + r) is the growth factor,r is the growth rate.

You Try:

Your business had a profit of \$25,000 in 1998. If the profit increased by 12% each year, what would your expected profit be in the year 2010?

C = \$25,000

T = 12

R = 0.12

Writing an Exponential Growth Model

A population of 20 rabbits is released into a wildlife region.

The population triples each year for 5 years.

What is the population after 5 years?

SOLUTION

After 5 years, the population is

P = C(1 + r)t

Exponential growth model

= 20 • 35

= 4860

There will be about 4860 rabbits after 5 years.

EXPONENTIAL DECAY MODEL

WRITING EXPONENTIAL DECAY MODELS

C is the initial amount.

t is the time period.

y = C (1 – r)t

(1 – r) is the decay factor,r is the decay rate.

Example: Depreciation
• You buy a new car for \$22,500. The car depreciates at the rate of 7% per year,
• What was the initial amount invested?
• What is the decay rate? The decay factor?
• What will the car be worth after the first year? The second year?
• The initial investment was \$22,500.
• The decay rate is 0.07. The decay factor is 0.93.
You Try:

Iodine-131 is a radioactive isotope used in medicine. Its half-life or decay rate of 50% is 8 days. If a patient is given 25mg of iodine-131, how much would be left after 32 days or 4 half-lives.

C = 25 mg

T = 4

R = 0.5

Continuous Compounding

• We can compound every instant (i.e., continuously):
• Here, F is the future value, P is the present value, r is the annual rate of interest, t is the total number of years, and e is a constant equal to about 2.718

clem.mscd.edu/~mayest/FIN3300/Files/ch5.ppt

Example:

• Suppose that the Fourth National Bank is offering to pay 10% per year compounded continuously. What is the future value of your \$1,000 investment?

clem.mscd.edu/~mayest/FIN3300/Files/ch5.ppt

Example:

• Suppose that the Fourth National Bank is offering to pay 10% per year compounded continuously. If you plan to leave the money in the account for 5 years, what is the future value of your \$1,000 investment?

clem.mscd.edu/~mayest/FIN3300/Files/ch5.ppt

Homework

p.456,

#4, 5, 6, 8, 9, 12