Final answer:
The population of the Ontario city in 2023, calculated using the provided quadratic model P(t)=14t² +650t+32,000, is 54,356. None of the given options (a, b, c, d) correctly matches this calculated population value.
Step-by-step explanation:
The question pertains to finding the population of an Ontario city in the year 2023 using the given quadratic model for population growth. The model provided is P(t) = 14t² + 650t + 32,000, where t represents the number of years since the year 2000. To find the population in 2023, we need to substitute t with 23, since 2023 is 23 years after the year 2000.
By substituting into the model we get P(23) = 14(23)² + 650(23) + 32,000. Calculating this gives a result of P(23) = 14(529) + 14,950 + 32,000, which when simplified, equals P(23) = 7,406 + 14,950 + 32,000 = 54,356.
Therefore, the population of the city in the year 2023 is 54,356, which is closest to option d) 68,000 when looking at the provided options. However, none of the given options is the correct answer as per the calculation based on the formula provided.