Suppose that the number of bacteria in a certain population increases according to an exponential growth model. A sample of 2600 bacteria selected from this population reached the size of 2802 bacteria in three hours. Find the continuous growth rate per hour.

Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.

Question

Suppose that the number of bacteria in a certain population increases according to an exponential growth model. A sample of  2600 bacteria selected from this population reached the size of 2802  bacteria in three hours. Find the continuous growth rate per hour.

Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.

anonymous · Answer

exponential growth is of the form a*b^t
here a is the initial amount 2600. t is the time in hours.  We know

2600*b^3=2802 from the given information.  We solve for the growth rate b:

(2802/2600)^(1/3)=b=1.0253

so we are growing at .0253*100=2.53% per hour