Answer:
Option (c) is correct.
function representing the increase of bacteria every hour x,
Step-by-step explanation:
Given : A colony contains 1500 bacteria. The population increases at a rate of 115% each hour.
we have to find the function that represents the given scenario.
Let x represents the number of hours elapsed.
Given A colony contains 1500 bacteria
and number of bacteria is increasing at a rate of 115% each hour.
Using formula for Compound interest , we have,
![A=P(1+\frac{r}{100} )^t](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7B100%7D%20%29%5Et)
Where A is amount
T is time period
R is rate of interest
Here, P = 1500
T = x hours
R = 115%
Let f(x) be the function representing the increase of bacteria every hour.
Substitute, we have,
![f(x)=1500(1+\frac{115}{100} )^x](https://tex.z-dn.net/?f=f%28x%29%3D1500%281%2B%5Cfrac%7B115%7D%7B100%7D%20%29%5Ex)
Simplify, we get,
![f(x)=1500(1+1.15)^x](https://tex.z-dn.net/?f=f%28x%29%3D1500%281%2B1.15%29%5Ex)
![f(x)=1500(2.15)^x](https://tex.z-dn.net/?f=f%28x%29%3D1500%282.15%29%5Ex)
Thus,
function representing the increase of bacteria every hour x,