Question

The population of a city can be modeled by the equation y = 12,500(1.03)^x where x is the number of years since 1965. Determine the estimated population for 2006.

A. 52,195
B. 45,100
C. 41,999
D. 38,611

Answer 1

To estimate the population for 2006 using the model y = 12,500(1.03)^x, we calculate x as 41 years since 1965. Plugging x into the equation gives an estimated population of approximately 38,611 for the year 2006, matching option D.

Step-by-step explanation:

To determine the estimated population of the city for the year 2006 using the given model y = 12,500(1.03)^x, where x is the number of years since 1965, we first calculate the value of x for 2006. Subtracting the base year, 1965, from 2006 gives us x = 2006 - 1965 = 41 years. Next, we plug this value into the equation to calculate y:

y = 12,500 × (1.03)^41

Using a calculator, we find that y is approximately 38,611 when rounding to the nearest whole number. Thus, the estimated population for the city in 2006 is about 38,611, which corresponds to option D.