An antibiotic kills 60 percent of bacteria in a sample of 100 comma 000 each day. The equation p sub 1 is equal to 100 comma 000 times 0 point 4 to the d th power represents the population, p sub 1 , after d days. Four days after introducing the antibiotic to the first sample, a scientist introduces the same antibiotic to a second population, p sub 2 The number of bacteria after d days in the second population is represented by the equation p sub 2 is equal to 100 comma 000 times 0 point 4 raised to the d minus 4 power Which equation is equivalent to p sub 2 ?
Answer
A
p sub 2 is equal to 100 comma 256 times 0 point 4 to the d th power
B
p sub 2 is equal to 99 comma 744 times 0 point 4 to the d th power
C
p sub 2 is equal to 3 comma 906 comma 250 times 0 point 4 to the d th power
D
p sub 2 is equal to 2 comma 560 times 0 point 4 to the d th power
Explanation
Use the exponent rule to rewrite 0.4^(d − 4) as 0.4^d × 0.4^(−4). Since 0.4^(−4) = 1 ÷ 0.4^4 = 1 ÷ 0.0256 = 39,062.5, the coefficient becomes 100,000 × 39,062.5 = 3,906,250. Thus the equivalent equation is p₂ = 3,906,250 × 0.4^d, choice C.
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