Answer:
![a(15)=4(3)^{15}](https://tex.z-dn.net/?f=a%2815%29%3D4%283%29%5E%7B15%7D)
Explanation:
Given,
Original number of bacterial cell = 4,
Also, the number of bacterial cell triples every month,
So, the number of bacteria after one month = 3 × 4 = 4(3)
After two months = 3 × 4(3) = 4(3)²,
After three months = 3 × 4(3)² = 4(3)³,
......................................................... , so on,
Thus, the number of bacterial cell after 15 months,
![a(x)=4(3)^x](https://tex.z-dn.net/?f=a%28x%29%3D4%283%29%5Ex)
For 15 months, x = 15,
Hence, the number of bacterial cells after 15 months,
![a(15)=4(3)^{15}](https://tex.z-dn.net/?f=a%2815%29%3D4%283%29%5E%7B15%7D)
Which is the required equation she should use.