an object is dropped from a building and allowed to freefall to the ground. the height of the object over time is shown in the table. ( for reference h(t)= 144-16^2 )
answer
D. the rate of change increases over time. the object drops 16 feet in the first second, but 80 feet in the last second.
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Which is the graph of f(x)= 0.5 (4)^x ?
answer
A.
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A limited-edition poster increases in value each year. After 1 year, the poster is worth $20.70. After 2 years, it is worth $23.81. Which equation can be used to find the value, y, after x years? ( round money values to the nearest penny. )
answer
A. y=18 (1.15)^x
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what is the multiplicative rate of change of the function shown on the graph? express your answer in decimal form. round to the nearest tenth.
(-1,0.8)(0,2)(1,5)(2,12.5)
answer
2.5
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what are the domain and range of the function on the graph?
answer
D. the domain includes all real numbers, and the range is y > 0
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A function of the form f (x) = ab^x is modified so that the b value remains the same but the a value is increased by 2. how do the domain and range of the new function compare to the domain and range of the original function? Check all that apply.
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A. the range stays the same.
C. the domain stays the same.
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Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equation represents the amount of money in Josiahs account, y, after x years?
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D. y = 360 (1.03)^x
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Which equation represents an exponential function that passes through the point (2,80)?
answer
f (x) = 5 (4)^x
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Geraldine is asked to explain the limits on the range of an exponential equation using the function f (x)=2^x. She makes these two statements:
1. As x increases infinitely, the y-values are continually doubled for each single increase in x.
2. As x decreases infinitely, the y-values are continually halved for each single decrease in x.
answer
D. the conclusion is incorrect because the range is limited to the set of positive real numbers.
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Keshawn is asked to compare and contrast the domain and range for the two functions.
f (x)=5x
g (x)=5^x
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A. the domain of both functions is all real numbers.
F. the range of g (x) is y > 0
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what is the rate of change of the function described in the table?
x= -1,0,1,2,3
y= 1/10, 1/2, 5/2, 25/2, 125/2
answer
B. 5
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Which is the graph of f (x)= 1/4 (4)^x?
answer
D.
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Which table represents exponential growth?
answer
B. x= 1,2,3,4
y= 2,4,8,16
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Which equation represents an exponential function that passes through the point (2,36)?
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A. f (x)= 4 (3)^x
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the value of a collector's item is expected to increase exponentially each year. the item is purchased for $500. After 2 years, the item is worth $551.25. Which equation represents y, the value of the item after x years?
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B. y= 500 (1.05)^x
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Which equation represents an exponential function with an initial value of 500?
answer
C. f (x)= 500 (2)^x
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Which is the graph of f (x)= 5 (2)^x?
answer
A.
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Which best describes the graph of the function f (x)= 4 (1.5)^x ?
answer
B. the graph passes through the point (0,4), and for each increase of 1 in the x-values, the y-values increase by a factor of 1.5.
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