Jazmine G.
asked • 12/20/16which of the following equations represents a graph that decreases most rapidly?
A. y=-2*2^x-24 B. y=-3*2^x+16 C. y=-1/2*2^x-4 D. y=-1*2^x+12
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2 Answers By Expert Tutors
Gregg K. answered • 12/21/16
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Effective Math Tutor Specializing in AP Calculus AB/BC , AP Statistics
They all decrease at the same rate
Kenneth S.
I think gregg's answer is untrue.
consider this table, which shows y values for each function, when x=0 & when x=1
function: A B C D
when x=0 -26 13 -4.5 11
when x=1 -28 10 -5 10
Here are the decreases for A, B, C, D as x goes from 0 to 1:
2 3 ½ 1
Does this convince you that "B" decreases the most?
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12/21/16
Gregg K.
tutor
Let's look at the ratio of function values rather than the difference of function values to determine the answer. As X gets large the ratio of function values is the same for all functions for consecutive integers
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12/21/16
Gregg K.
tutor
For small values of x Let's ignore the constants on the end as stated above and the ratio of function values is the same for all functions we do not have to ignore this constant as X gets large because as X gets large this constant becomes negligible
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12/21/16
Kenneth S. answered • 12/20/16
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Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018
All of these equations are exponential in nature, but the exponential term has a different negative coefficient in the four equations (the constants at the end of each expression have no effect on rate of decrease).
Because the "B" equation has the most negative leading coefficient, its rate of decrease is the greatest.
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Philip P.
12/20/16