Answer:
The exponential function is ![C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1](https://tex.z-dn.net/?f=C%28t%29%3Dy%28b%29%5Et%5C%20Or%5C%20C%28t%29%3D1800%281.15%29%5E1)
Step-by-step explanation:
Given
be the number of hours.
number of bacteria cells.
And we know that an exponential function is
,where
is a positive real number, and in which the argument
occurs as an exponent
The petri dish has
bacteria cells we can say that ![y=1800](https://tex.z-dn.net/?f=y%3D1800)
In the equation as
is function of time and
will vary as
for respective hours.
To find the value of
we have to understand that it is dependent on percent increase if there is increment of
then ![b=1+15\%=1+\frac{15}{100}=1+0.15=1.15](https://tex.z-dn.net/?f=b%3D1%2B15%5C%25%3D1%2B%5Cfrac%7B15%7D%7B100%7D%3D1%2B0.15%3D1.15)
So the exponential function will be
,plugging the values it will be equivalent to ![C(t)=1800(1+0.15)^1](https://tex.z-dn.net/?f=C%28t%29%3D1800%281%2B0.15%29%5E1)
Check:
![15\% of 1800 =0.15\times 1800=270](https://tex.z-dn.net/?f=15%5C%25%20of%201800%20%3D0.15%5Ctimes%201800%3D270)
So in first hour the cells will increased by a quantity of
cells.
The number of cells after an hour in the petri dish ![=(1800+270)=2070](https://tex.z-dn.net/?f=%3D%281800%2B270%29%3D2070)
That can also be from the formula.
![C(t)=1800(1.15)^1=2070](https://tex.z-dn.net/?f=C%28t%29%3D1800%281.15%29%5E1%3D2070)
So the exponential function is ![C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1](https://tex.z-dn.net/?f=C%28t%29%3Dy%28b%29%5Et%5C%20Or%5C%20C%28t%29%3D1800%281.15%29%5E1)
will increase exponentially as the value of
increase.