Exponential Growth in Fruit Fly Population
The image contains a math problem regarding exponential growth. The problem is as follows:
"15,000 fruit flies were released into the Western River for a scientific study. The function N(t) = 15,000(3^t) represents the number of blue-tailed fruit flies after t years. What would happen to this population?"
The options are:
A) It will decrease by about 2,000.
B) It will decrease by about 3,000.
C) It will increase by about 2,000.
D) It will increase by about 3,000.
The function provided, N(t) = 15,000(3^t), models exponential growth. As t increases, N(t) also increases since 3^t is always greater than 1 for any positive t. Therefore, the population will increase over time, not decrease.
Since no specific time frame is given in the question or the options (like t = 1 year or 5 years), we cannot calculate the exact amount of increase. Nonetheless, we can definitively say that the population will increase, not decrease.
The correct answer to what will happen to this population is between either option C or D (since options A and B are about a decrease), and without additional context or a specific time frame (value of t), we cannot determine the exact amount of increase from the options provided. However, given that the question implies a short period (probably a year), the increase would be substantial due to the nature of exponential growth, which would suggest option D is more likely. But to reiterate, without a specific time frame mentioned in the problem, the exact numerical increase cannot be determined from the options given.
