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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  . Which of the following statements is not correct? |
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Choose:
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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? |
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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) |
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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?
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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? |
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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. |
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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.
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What will be the value of b if the model is re-written as
P(t) = 22456(b)t ?
Choose:
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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.) |
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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:
b) If the yearly rate of loss should continue through 2017, what would be the rate of loss over this three year period?
Choose:
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FYI: The normal yearly rate of loss of honeybees, prior to 2015, was 18.7%.
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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. [1.27 is the yearly growth factor; t is the number of time increments]
Meanwhile, 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. [0.87 is the yearly decay factor and t is the number of time increments]
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| 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.
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| 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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