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answer:
N(t)=2×
17
15
step by step explain:
before lesson (t=0), she knows 2 words.
after a week (t=1), she knows
2×(1+70%)=3.4 words
after one more week (t=2), she knows
3.4×(1+70%)=5.78 words
one more week later (t=3), she knows
5.78×(1+70%)=9.826 words
and so on ...
from pattern shown above, we know that she knows
2× words after t weeks
so N(t)=2×
after 4 weeks (t=4), she knows 2×=16.7042≈17 words
for learning 5000 words, she need:
2×=5000
=2500
t log(1.7)=log(2500)
t=
=14.7448727
≈15 (round up)