Answer:
[tex]P(t)= 100e^{1.335t}[/tex]
Step-by-step explanation:
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size.
Formula for the exponential growth is
[tex]A= A_0e^{rt}[/tex]
where A0 is the initial cells (100) and t is the number of hours
[tex]A= 100e^{rt}[/tex]
After an hour the population has increased to 380
when t=1 the value of A is 380
[tex]380= 100e^{r(1)}\\\\\frac{380}{100} =e^r\\\\[/tex]
Take ln on both sides
r=1.33500
[tex]A= 100e^{rt}\\A= 100e^{1.335t}[/tex]
[tex]P(t)= 100e^{1.335t}[/tex]
