In planning maintenance for a city's infrastructure, a civil engineer estimates that, starting from the present, the population of the city will decrease by 10 percent every 20 years. If the present population of the city is 50,000, which of the following expressions represents the engineers estimate of the population of the city t years from now?
In planning maintenance for a city's infrastructure, a civil engineer estimates that, starting from the present, the population of the city will decrease by 10 percent every 20 years. If the present population of the city is 50,000, which of the following expressions represents the engineers estimate of the population of the city t years from now?
The correct option is D 50,000(0.9)t20
For the present population to decrease by 10 percent,
it must be multiplied by the factor (1−10100)=(1−0.1)=0.9. Since the engineer estimates that the
population will decrease by 10 percent every 20 years, the present
population, 50,000, must be multiplied by(0.9)n, where n is the number of 20‑year periods that will
have elapsed t years from now.
After t years, the number
of 20‑year periods that have elapsed is t20.
Therefore, 50,000(0.9)t20 represents the
engineer’s estimate of the population of the city t years from now.
For the present population to decrease by 10 percent, it must be multiplied by the factor (1−10100)=(1−0.1)=0.9. Since the engineer estimates that the population will decrease by 10 percent every 20 years, the present population, 50,000, must be multiplied by(0.9)n, where n is the number of 20‑year periods that will have elapsed t years from now.
After t years, the number
of 20‑year periods that have elapsed is t20.
Therefore, 50,000(0.9)t20 represents the engineer’s estimate of the population of the city t years from now.
