# System of algebraic equations concerning rates

I'm not even sure where to start on the problem. Is this possible to solve without logarithms?

"A certain type of bacteria doubles every 6.5 hours. If there were 60 bacteria to start with, what is the hourly growth rate of the bacteria? How many bacteria will there be after a day and a half? Solve using algebra."

• What do you know about geometric progressions. That could be somewhere to start. – Allawonder Apr 19 at 9:34
• Can you write down a formula that expresses the fact the the population doubles in $6.5$ hours? That seems like the place to start to me. – saulspatz Apr 19 at 14:05
• $\ t = b2^{t/20}$? – finky1234 Apr 19 at 14:09
• After $t$ hours there are $60\cdot2^{x/6.5}$ bacteria. Does that help? – Michael Hoppe Apr 19 at 14:13
• What other equation do I have to write from there? – finky1234 Apr 19 at 14:14