A student was trying to write an exponential function to represent a fish population in a local stream decreasing at a rate of 4% per year. The original population was 48,000. The student made an error when writing their exponential function.
Find and explain the error in the student’s work below. Student’s answer: y = 48,000(1.04) Type your answer in the box below.
The error in the student's work is that they used a growth factor of 1.04 instead of a decay factor. Since the fish population is decreasing at a rate of 4% per year, the correct decay factor should be 0.96 (100% - 4% = 96%). Therefore, the correct exponential function should be:
y = 48,000(0.96)