Answer:
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
[tex]A=Pe^{rt}[/tex]
where A = total number of bacteria, P = initial number of bacteria, r= rate of change , t= time
[tex]228=16(e^{4r})[/tex]
[tex]14.25=(e^{4r})[/tex]
Taking log both side,
[tex]log(14.25)=4r[/tex]
[tex]1.15=4r[/tex]
[tex]0.28=r[/tex]
Therefore, Rate of change per hour in the number of bacteria is r=0.28
