A scientist counts 35 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y=35*3^x models the number of bacteria after x hours. ??? How can I estimate when there will be about 500 bacteria.

Question

anonymous · Answer

Since we are estimating for 500, y=500
Take logarithms on both sides of the equation:$$\log_{10}500=\log_{10}(35) +\log_{10}({3^{x})}    $$
Take log35 to the otherside and then according to the rules of logs. Divide by log 3 on both sides since the $$\log_{10}(3^{x} )$$ becomes$$x \log_{10} 3$$

x=(log500-log35)/log3
x=2.42 hours approximately to 3 significant figures.

anonymous · Answer

Hey,Mr.IceCream so ur saying that x=3

anonymous · Answer

It depends on how precise the answer needs to be. Otherwise I'm saying x=2.42 hours

anonymous · Answer

about 2.5 hours if you round up