Practice Page
Directions: Read very carefully and choose the best answer. Assume a "month" to be of a constant size. (Don' t worry about months containing different numbers of days.)

1.
A collector purchases an antique vase. An equation to represent the value, A, of the antique vase after m months of ownership is vasecost. Which of the following statements is not correct?
Choose:
The value of the vase when it was purchased
     was $5,000.
The vase gains approximately 24% of its value
     each month.
The vase increases in worth by approximately
     102% of its value each month.
The value of the vase one year after it was
     purchased was $6,200.

 

 

2.
A population of bacteria, during a one year study, grew according to the model
B = B0(1.75)t, where B is the population, B0 is the starting population, and t is the time in years. Using 52 weeks in a year, which of the choices will model the approximate weekly growth rate?
Choose:
 
Nexp8a
Nexp8b
 
Nexp8c
Nexp8d

 

 

3.
The Speedy Foot Shop has been selling a newly designed skateboard. The board has been very popular and the shop has seen a 4.25% increase in profits over the past year. If this trend continues, which expression could the shop use to approximate the monthly percent increase in profits? (m stands for months)
Choose:
 
(1.0425)m
(1.0425)12/m
 
(1.00347)m
(1.00347)12/m

 

 

4.
The growth rate of a new strain of bamboo plants is modeled by the function,
F(t) = 120(1.28)t, where t represents the number of years since the plants were germinated. Which choice best represents the monthly growth rate of the plants?
bamboo
Choose:
 
F(t) = 120(1.28)t/12
F(t) = 120(1.02)t/12
 
F(t) = 120(1.28)12t
F(t) = 120(1.02)12t

 

 

5.
Manuel found a gold coin from Captain Jack Sparrow's sunken ship, the Black Pearl. A collector told him that the coin is appraised for $200, and that the estimated value after t years can be calculated using the formula
G(t) = 200(1.05)t. Which choice shows the percent by which the coin is increasing each year?
Choose:
 
5%
50%
95%
105%

 

 

6.
Last year, the total revenue for a national restaurant chain increased by 5.25% over the previous year. If this trend continues, which expression could the company's financial officer use to approximate the monthly percent increase in revenue? Let m represent months.
Choose:
 
(1.0525)m
(1.00427)m
 
Regents24a
Regents24b

 

 

7.
A city has a population of 22,456 in the year 2016. A highway has directed traffic away from the quaint old city. Research shows that the population is decreasing every four years according to the model P(t) = 22456(0.95)4t.
city2
  What will be the value of b if the model is re-written as
P
(t) = 22456(b)t ?
Choose:
 
0.81
0.95
0.99
1.05

 

 

8.
A farmer discovers that he has 20 small brown mice in his barn. The mice population doubles every four months according to the formula
M(t) = 20(2)3t, where t is years since finding the 20 mice. After how many months will there be 1000 mice in the barn? (Assume none of the mice die, and round to the nearest integer.)
Choose:
 
2 months
12 months
 
21months
23 months

 

 

9.
In 2015, the US experienced a dramatic loss of honeybees, with 42.1% of the colony bees being lost within a 12 month period.
a)
What was the monthly rate of loss during this one year period?
Choose:
 
4.45%
42.1%
 
57.9%
95.5%

b)
If the yearly rate of loss should continue through 2017, what would be the rate of loss over this three year period?
Choose:
 
19.4%
21.6%
 
57.9%
80.6%
bees
FYI: The normal yearly rate of loss of honeybees, prior to 2015, was 18.7%.


 

 

10.
Widgets are increasing in popularity and their inventory can be modeled by the function W(t) = 300(1.27)5t over a 5 year period. At the same time Gidgets are decreasing in popularity and their inventory can be modeled by the function
G
(t) = 600(0.87)2t over a 2 year period.
a) Determine the 5-year rate of growth for W(t) and the 2-year rate of loss for G(t).
b) Create a function for each of these companies to examine the yearly inventory related to rate of growth or decay.
c) Graph the two new functions and determine the point of intersection of the two graphs. What does this intersection point show?



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