Can anyone solve this using the "completing the square" method? (or something similar)
1 answer:
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Answer:
<em>11 years</em>
Step-by-step explanation:
This is a case of exponential decay.
Let n = number of years; p = population after n years; a = initial population; r = rate of decay
p = a(1 - r)^n
Now we substitute the numbers we know leaving n as the only unknown.
100 = 250(1 - 0.08)^n
100 = 250(0.92)^n
Divide both sides by 250.
0.4 = 0.92^n
Take the log base ten of each side.
log 0.4 = log 0.92^n
Use log rule: log a^n = n * log a
log 0.4 = n * log 0.92
Divide both sides by log 0.92
n = 10.989
Answer: 11 years