Other Models

What we have learned

Exponential Growth Model n(t)=n0 at, a>1

Exponential Decay Model n(t)=n0 at, 0<a<1

Logarithmic Model

y = a + b lnt Growth if b>0 Decay if b<0

Logarithmic Model

The number of endangered animal species in the United States from 1990 to 2002 can be modeled byy = -119 +164 ln t, 10 ≤ t ≤ 22, where represents the year, with t = 10 corresponding to 1990. During which year did the number of endangered animal species reach 357?

pH Value

Chemist use the pH value to describe the acidity of a solution. It is given by the formula:pH = - log[H+], where [H+] is measured in moles of hydrogen ions per liter in the solution. Find the pH of a solution with [H+] = 0.0063

moles per liter. Find the amount of hydrogen ions [H+] in moles

per liter of a solution with pH = 6.6.

Logistic Model

1 rt

ay

be

Growth Model

ya, as t∞ Grows fastest when

y=a/2

Logistic Model

On a college campus of 5000 students, one student returns from vacation with a contagious and long-lasting flu virus. The spread of the virus is modeled by

How many students will be infected after 5 days?

At what time is the flu spreading at the fastest rate?

The campus will close if more than 55% of students are infected. After how many days will the campus close?

Irregular Models

The relationship between the price (p) and the demand (d) for a hand-held electronic organizer is given by the demand equation:

0.002

45000 1

4 dp

e

Find the price when the demand is 800 units.

Find the demand if the price is set to be $1000 per unit.

0 500 1000 1500 2000

200

400

600

800

1000

Demand for Carb is banned in Texas

Fin…