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

the answer is 2.5 hours

Answer 2

`y = 25\cdot~3^x\\ \\ 1170 = 25\cdot~3^x\\ \\ (1170)/(25) = 3^x\\ \\ (243)/(5) = 3^x\\ \\ log\ (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=(1,7)/(0,48)\\ \\ \large{\boxed{x=3,54\ h}}`