Question

A scientist counts 25 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y = 25 ∙ 3x models the number of bacteria after x hours. Estimate when there will be about 1170 bacteria in the culture

Answer 1

$y = 25\cdot~3^x\\ \\ 1170 = 25\cdot~3^x\\ \\ \frac{1170}{25} = 3^x\\ \\ \frac{243}{5} = 3^x\\ \\ log\ \frac{243}{5} = log~3^x\\ \\ log~243-log~5=x~log~3\\ \\ log~3^5-log~5=x~log~3\\ \\ 5~log~3-log~5 = x~log~3\\ \\ 5(0,48)-0,70= 0,48x\\ \\ 2,4-0,7 = 0,48x\\ \\ 1,7=0,48x\\ \\ x=\frac{1,7}{0,48}\\ \\ \large{\boxed{x=3,54\ h}}$

Answer 2

the answer is 2.5 hours