- #1
XJellieBX
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Question:
A new disinfectant spray is expected to kill 50% of the known germs in a room, but for health reasons it can only be used once a day. Between spraying, the germs increase by 25%. How many consecutive days of spraying are required to reduce the germs in the room to 10% of the original amount?
Relevant equations:
A=Ao(1+i)^n
Attempt:
0.10Po=Po(0.50)^d + 0.25Po(0.50)^d
0.10=0.50^d + 0.25(0.50)^d
0.10=1.25(0.50)^d
0.08=0.50^d
log0.08=log0.50^d
log0.08=dlog0.50
d=[tex]\frac{log0.08}{log0.50}[/tex]
d=4
Can someone please tell me what I'm doing wrong? The answer is supposed to be 5 days.
A new disinfectant spray is expected to kill 50% of the known germs in a room, but for health reasons it can only be used once a day. Between spraying, the germs increase by 25%. How many consecutive days of spraying are required to reduce the germs in the room to 10% of the original amount?
Relevant equations:
A=Ao(1+i)^n
Attempt:
0.10Po=Po(0.50)^d + 0.25Po(0.50)^d
0.10=0.50^d + 0.25(0.50)^d
0.10=1.25(0.50)^d
0.08=0.50^d
log0.08=log0.50^d
log0.08=dlog0.50
d=[tex]\frac{log0.08}{log0.50}[/tex]
d=4
Can someone please tell me what I'm doing wrong? The answer is supposed to be 5 days.