Average Value of a Function
I'm working on a school assignment and need someone to check it.
The growth rate for a 24-hour period of a bacteria colony is measured to be r(t)=96e^(.24t), where r(t) is measured in bacteria per hour. At t=0, there are 400 bacteria in the colony. Find the average groth rate for the time period 0 equal to or less than t equal to or less than 24.
How many bacteria would be in the colony at the end of the 24-hour period?Include units.
integral with bounds [24,0] 96e^(.24t)
integral ==> 400e^(.24t)
400e^(.24(24)) - 400e^(.24(0)) = 126539 bacteria per hour.
126539 * 24=3036944 bacteria per day.
Is this the correct solution? My other solution was to solve for
r(0)+integral with bounds [24,0] 96e^(.24t). I added the r(0) because it's the initial bacteria count.
Sorry it's a little hard to read.