Question

The population p in thousands of a city t years from now is modelled by p(t) = t3 t2 "-2t" 10. city council decides that when the population has quadrupled its current value, construction of new homes will be limited. when will this limit take place

Answer 1

The mathematics question asks when the population of a city will quadruple based on a polynomial model. To find the answer, determine the initial population, then solve for the time at which the population will be four times the initial value using the provided polynomial equation.

Step-by-step explanation:

The question involves determining when the population of a city will quadruple based on a given polynomial model p(t) = t^3 + t^2 - 2t + 10, where p(t) represents the population in thousands and t represents the number of years from the present. To answer this question, the current population must be determined by plugging in t = 0 into the polynomial equation, then multiplying this value by four to find the population goal. Then, the population model equation is solved for t using the quadrupled population as the new value for p(t).

To solve for t when the population has quadrupled, you would typically set the polynomial equation equal to four times the initial population and solve for t. However, given that the written polynomial is potentially incorrect due to the inconsistent notation and the phrase "-2t" appears quoted, a clarification should be sought from the student regarding the correct expression for the population model before solving.