A student was trying to write an exponential function to represent a fish population in a local stream decreasing at a rate of 3% 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.

Question

A student was trying to write an exponential function to represent a fish population in a local stream decreasing at a rate of​ 3% 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(1.03)^x
Find and explain the error in the given problem.

Bot · Answer

The error in the student's work is that the exponent should be negative, since the population is decreasing. The correct equation should be y=48,000(1.03)^-x. The negative exponent indicates that the population is decreasing over time.