Answer:
[TeX] y=2900e^{1.18t} [/TeX]
Explanation:
The exponential gwoth function is given as:
[TeX] N=N_{o}e^{rt} [/TeX]
Where N(t)=Number of bacteria at time t.
[TeX] N_{o}[/TeX] =Initial Population.
r=Growth Rate; and
t=time.
To begin a bacteria study, a petri dish had 2900 bacteria cells.
Therefore:[TeX] N_{o}=2900[/TeX]
t= number of hours since the start of the study.
The number of cells have increased by 18%.
Therefore the growth rate, r =100%+18%=118%=1.18
We are asked to represent y as the number of bacteria cells at any time t.
Therefore the function showing the relationship between y and t is given as:
[TeX] y=2900e^{1.18t} [/TeX]