Using the exponential growth formula, the number of bacteria in the petri dish after 5 months is approximately 345, after starting with 246 bacteria and growing at a rate of 7% per month.
To calculate the number of bacteria in a petri dish after 5 months with an initial amount of 246 bacteria and a growth rate of 7% per month, we can use the formula for exponential growth:
N = P(1 + r)^t
Where:
- N = New amount after time t
- P = Initial principal amount (initial number of bacteria)
- r = Monthly growth rate (as a decimal)
- t = Time (number of months)
For this problem:
- P = 246
- r = 7% or 0.07
- t = 5 months
Let's plug these values into the formula:
N = 246(1 + 0.07)^5
N = 246 * (1.07)^5
N ≈ 246 * 1.402552
N ≈ 344.8272
The number of bacteria after 5 months, rounded to the nearest whole number, is approximately 345. Therefore, the correct answer is B) 345.