Name:___________________________________________

1. Calculate the new price if the old price of $ 69.50 is decreased by 7.5%.

 

 

New Price =$64.29
 

2. Calculate the old price if the new price is $75.00 after the old price was reduced by 12 %.

 

 

Old Price = $85.23
 
 

3. The edge of a square is 10 inches. By what percentage must its edge be increased in order to increase the area A = x² by 25%?

 

 

% increase of edge = 11.8%
 

4. In each of the following problems give the formula for the population P as a function of the time t.

• The initial population of 55 doubles every year.

 

 

P(t) = 55*2^t
 

• The initial population of 100 triples every 4 years.

 

 

P(t) = 100*3^(t/4)
 

• The initial population of 75 increases by 4.5% each year.

 

 

P(t) = 75*1.045^t
 

• The initial population of 120 decreses by 8% per year.


            P(t) = 120*.92^t
 

• P(2) = 200 and P(4) = 240


P(t) = 166.67*(6/5)^(t/2)

5. Suppose you invest $8,000. Find the interest rate r your investment must earn in order to double your money in 12 years. Calculate the interest rate to 4 decimal places. You may solve with algebra, intersection of graphs, or repeated tabulation. Recall that r is the independent variable in the equation 

6. The population of Africa was 375 million in 1970 and 491 million in 1980. Assuming a natural population growth, find the following,

• The annual growth factor (multiplier)


1.02732
 

• The annual percent increase in population.


2.732%
 
 
 
 

• The population model.


P(t) = 375*1.02732^t
 
 

• The year in which the population will reach 700 million.

7. The table below gives data from a function that is exactly exponential. Find a function of the form that fits these points exactly.

Function: y = 2^x
 
 

8. The atmospheric pressure p ( in pounds per square inch) is a naturally declining function of the altitude x above sea level. The following table gives and p for several values of x.

1. Find the exponential model that best fits the data.

 

 

Exponential Model

14.699969*.96275^x
 

2. At what altitude does the pressure reach 7.5 lb/ in² (the minimum pressure at which an average human can survive)

 

 

Altitude when p = 7.5
17.73 thousand feet
 
 

3. Mount Everest has an altitude of 29,035 ft.. What is the pressure at this altitude?


Pressure on Everest
4.88 bs. Per Square inch
 
 
 

4. Complete the above table.

 

 

5. Find the average error in the model.r