Answer:
It takes at least 7 months for the cat to be at least 6 kg lighter than the original weight.
Step-by-step explanation:
Use exponential decay formula:
A = P (1-r)t
A = amount decreased to
P = original amount
r = rate of decrease
t = time
Â
6 ≥ 12 (1-0.10)t    divide both sides by 12
0.5 ≥ (0.9)t       take log of both sides
log (0.5) ≥ log (0.9)t   power rule of logs lets the exponent t drop to front of log to become a factor
log (0.5) ≥ t log(0.9)   divide both sides by log(0.9) which is negative so reverse the inequality sign
log (0.5) / log (0.9) ≤ t   use calculator
6.57 ≤ t
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It takes at least 7 months for the cat to be at least 6 kg lighter that original weight.
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check:
12 (0.9)7≈ 5.73
12 (0.9)6 ≈ 6.37
