Question

Choose among these options the one that results in a graph that shows exponential decay. A. f(x) = 0.6(2)x B. f(x) = 3(0.7)x C. f(x) = 0.4(1.6)x D. f(x) = 20(3)x

Answer 1

Answer: [B]: " f(x) = 3(0.7)ˣ " .
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x | y
0 | 3
1 | 2.1
2 | 1.48
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When, "x" [which is the exponent] increases" ; the resulting value; "y" on a graph, DECREASES; hence; "exponential decay".
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Consider Choice [A]: " f(x) = 0.6(2)ˣ " .
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x | y
0 | 0.6
1 | 1.2
2 | 2.4 ;

When "x" [the exponent] increases, the resulting value; "y" (on a graph); INCREASING; indicating 'exponential growth' ; NOT 'exponential decay' .
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Consider Choice [C]: "f(x) = 0.4(1.6)ˣ " .
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x | y
0 | 0.4
1 | 0.64
2 | 1.024

When "x" [the exponent] increases, the resulting value; "y" (on a graph); INCREASING; indicating 'exponential growth' ; NOT 'exponential decay' .

→ As such, Choice: [C]: is incorrect.
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Consider Choice [D]: " f(x) = 20 * (3)ˣ " ;
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x | y
0 | 20
1 | 60
2 | 180 ;
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When "x" [the exponent] increases, the resulting value; "y" (on a graph); INCREASING; indicating 'exponential growth' ; NOT 'exponential decay;.

→ As such, "Choice [D]" is incorrect.
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Answer 2

B. f(x) = 3(0.7)ˣ
Decay means an overall decrease in the original value. Exponential equations are written in the form:
amount after time n = original amount x (decay OR increase factor)ⁿ
The value of the factor is less than one in the case of a decay.