5. Functions A and B give the population of City A and City B. respectively, t years since 1990.In each function, population is measured in millions. Here are the graphs of the two functions. a. Which function value is greater: A(4) or B(4) b. Are there one or more values of t at which the equation A(t)=B(t) is true? If so, which one or which ones? C.Identify at least two values of t at which the inequality B(t)lt A(t) is true.

To answer these questions, we will analyze the given information about the population growth of City A and City B over time.a. To determine which function value is greater, \(A(4)\) or \(B(4)\), we need to estimate the population of both cities at years since 1990.For City A, the population increases from 2 million to 7 million over 12 years. This means the population increases by million over 12 years. To find the population at , we can estimate the population by dividing the total increase by the number of years and then multiplying by 4:Increase per year for City A = Population increase for City A at = For City B, the population increases from 2 million to 6 million over 12 years. This means the population increases by million over 12 years. To find the population at , we can estimate the population by dividing the total increase by the number of years and then multiplying by 4:Increase per year for City B = Population increase for City B at = Now let's calculate the population for both cities at :Population of City A at :\(A(4) = 2 + \frac{5}{12} \times 4 = 2 + \frac{5}{3} \approx 2 + 1.67 = 3.67\) millionPopulation of City B at :\(B(4) = 2 + \frac{4}{12} \times 4 = 2 + \frac{4}{3} \approx 2 + 1.33 = 3.33\) millionComparing the two populations:\(A(4) = 3.67\) million\(B(4) = 3.33\) millionTherefore, \(A(4)\) is greater than \(B(4)\).b. To find values of at which the equation \(A(t) = B(t)\) is true, we need to look for the point(s) where the two graphs intersect. According to the given information, both cities start with the same population of 2 million at . Therefore, at , \(A(t) = B(t)\). Since the populations are increasing and the rates of increase are different, there should be no other point where \(A(t) = B(t)\) if the lines do not cross again.Answer: The value of at which \(A(t) = B(t)\) is true is .c. To identify values of at which the inequality \(B(t) < A(t)\) is true, we need to find the time periods during which the population of City A is greater than that of City B. From the given information, we can see that after , City A's population is always greater than City B's population until . Therefore, any value of between 0 and 12 (excluding 0) will satisfy the inequality \(B(t) < A(t)\).Two such values could be and , as examples.Answer: Two values of at which \(B(t) < A(t)\) is true are and .