Final answer:
The number of bacteria in a colony increased by 150% over five hours, which corresponds to an average hourly increase of approximately 24.57% when considering exponential growth.
Step-by-step explanation:
To calculate the average percentage increase per hour of bacteria in a battery colony that increases by 150%, we can use the formula for exponential growth: Final amount = Initial amount * (1 + growth rate). Given that the number of bacteria increased by 150% in five hours, this means the bacteria multiplied by 2.5 times the original amount (100% + 150% = 250%, or 2.5 as a multiplier). To find the average growth rate per hour, we take the fifth root (since the growth happened over 5 hours) of 2.5 and subtract 1, then convert it to a percentage.
Let's perform the calculation:
- Calculate the fifth root of 2.5: (2.5)^(1/5).
- Subtract 1 from the fifth root.
- Multiply by 100 to get the percentage.
The fifth root of 2.5 is approximately 1.2457. Subtracting 1 gives us 0.2457. To convert this to a percentage, we multiply by 100, which equals 24.57% per hour. Thus, on average, the bacteria increases by about 24.57% per hour.