Final answer:
Using the polynomial model P(y) = 0.00018y⁴ + 0.0035y³ + 3.3, the predicted population for the city in the year 2023 is calculated to be 3.85 million people, assuming the provided trend continues.
Step-by-step explanation:
The student's question pertains to predicting the population of a city in a given year using a polynomial model. The model provided is P(y) = 0.00018y⁴ + 0.0035y³ + 3.3, where P(y) is the population of the city in millions, and y is the number of years since 2018. To predict the population in 2023, we substitute y with the number of years since 2018 until 2023, which is 5 years.
Calculating the population in 2023, we have:
P(5) = 0.00018(5)⁴ + 0.0035(5)³ + 3.3
Step 1: Calculate the power terms 5´ and 5³.
Step 2: Multiply these by their respective coefficients (0.00018 and 0.0035).
Step 3: Add up all terms, including the constant 3.3, to get P(5), the predicted population in 2023.
After carrying out these calculations:
P(5) = 0.00018(625) + 0.0035(125) + 3.3
P(5) = 0.1125 + 0.4375 + 3.3
P(5) = 3.85
The expected population of the city in 2023 is 3.85 million people, assuming the trend described by the polynomial model continues.