SOLUTION: The number bacteria growing in an incubation culture increases with time according to B(x)=8,200(5)^x, where x is time in days. After how many days will the number of bacteria in t

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Question 924551: The number bacteria growing in an incubation culture increases with time according to B(x)=8,200(5)^x, where x is time in days. After how many days will the number of bacteria in the culture be 205,000?
Found 3 solutions by josmiceli, josgarithmetic, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
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+B%28x%29+=+8200%2A5%5Ex+
given:
+B%28x%29+=+205000+
+205000+=+8200%2A5%5Ex+
+5%5Ex+=+2050%2F82+
+5%5Ex+=+25+
+5%5Ex+=+5%5E2+
+x+=+2+
In 2 days

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%28B%29%29=log%28%288200%2A5%5Ex%29%29
log%28%28B%29%29=log%28%288200%29%29%2Blog%28%285%5Ex%29%29
log%28%28B%29%29-log%28%288200%29%29%2Bx%2Alog%28%285%29%29|
log%28%28B%2F8200%29%29=x%2Alog%28%285%29%29
highlight%28x=%281%2Flog%28%285%29%29%29%2Alog%28%28B%2F8200%29%29%29

Evaluate x for B=205000.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The number bacteria growing in an incubation culture increases with time according to B(x)=8,200(5)^x, where x is time in days. After how many days will the number of bacteria in the culture be 205,000? 


B%28x%29+=+8200%285%5Ex%29

205000+=+8200%285%5Ex%29 ------ Substituting 205,000 for B(x)

205000%2F8200+=+5%5Ex

25+=+5%5Ex

5%5E2+=+5%5Ex

2 = x ------ Bases are equal, and so are the exponents

highlight_green%28highlight_green%28x+=+2%29%29 days