A scientist counts 25 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y=25 times 3x models the number of bacteria after x hours. Estimate when there will be about 1170 bacteria in the culture.
about 2.5 hours
about 5.5 hours
about 3.5 hours
about 4.5 hours
+26400 A scientist counts 25 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y=25 times 3x models the number of bacteria after x hours. Estimate when there will be about 1170 bacteria in the culture.
\(\begin{array}{rcl} y &=&25 \cdot 3^x \\ 1170 &=&25 \cdot 3^x \\ 25\cdot 3^x &=& 1170 \qquad & |\qquad : 25\\ 3^x &=& \frac{1170}{ 25 } \\ 3^x &=& 46.8 \qquad & |\qquad \log_{10}{}\\ \log_{10}{(3^x)} &=& \log_{10}{(46.8)} \\ x\cdot \log_{10}{(3)} &=& \log_{10}{(46.8)} \qquad & |\qquad : \log_{10}{(3)} \\ x &=& \frac{ \log_{10}{(46.8)} } { \log_{10}{(3)} }\\ x &=& \frac{1.67024585307} { 0.47712125472 }\\ \mathbf{x} &\mathbf{=}& \mathbf{3.50067375233} \end{array}\)
about 3.5 hours
+26400 A scientist counts 25 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y=25 times 3x models the number of bacteria after x hours. Estimate when there will be about 1170 bacteria in the culture.
\(\begin{array}{rcl} y &=&25 \cdot 3^x \\ 1170 &=&25 \cdot 3^x \\ 25\cdot 3^x &=& 1170 \qquad & |\qquad : 25\\ 3^x &=& \frac{1170}{ 25 } \\ 3^x &=& 46.8 \qquad & |\qquad \log_{10}{}\\ \log_{10}{(3^x)} &=& \log_{10}{(46.8)} \\ x\cdot \log_{10}{(3)} &=& \log_{10}{(46.8)} \qquad & |\qquad : \log_{10}{(3)} \\ x &=& \frac{ \log_{10}{(46.8)} } { \log_{10}{(3)} }\\ x &=& \frac{1.67024585307} { 0.47712125472 }\\ \mathbf{x} &\mathbf{=}& \mathbf{3.50067375233} \end{array}\)
about 3.5 hours
