Question

There are 16 bacteria in a beaker.Four hours later there are 228 bactriea in the beaker.What is the rate of change per hour in the number of bacteria.

Answer 1

Rate of change per hour in the number of bacteria is r=0.28

Step-by-step explanation:

Given : There are 16 bacteria in a beaker and four hours later there are 228 bacteria in the beaker.

To find : What is the rate of change per hour in the number of bacteria.

Solution :

At initial number of bacteria is 16

After 4 hours number of bacteria is 228

Rate of change per hour is given by

`A=Pe^(rt)`

where A = total number of bacteria, P = initial number of bacteria, r= rate of change , t= time

`228=16(e^(4r))`

`14.25=(e^(4r))`

Taking log both side,

`log(14.25)=4r`

`1.15=4r`

`0.28=r`

Therefore, Rate of change per hour in the number of bacteria is r=0.28