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 \(t = 4\) years since 1990.For City A, the population increases from 2 million to 7 million over 12 years. This means the population increases by \(7 - 2 = 5\) million over 12 years. To find the population at \(t = 4\), 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 = \(\frac{5 \text{ million}}{12 \text{ years}}\)Population increase for City A at \(t = 4\) = \(\frac{5}{12} \times 4\)For City B, the population increases from 2 million to 6 million over 12 years. This means the population increases by \(6 - 2 = 4\) million over 12 years. To find the population at \(t = 4\), 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 = \(\frac{4 \text{ million}}{12 \text{ years}}\)Population increase for City B at \(t = 4\) = \(\frac{4}{12} \times 4\)Now let's calculate the population for both cities at \(t = 4\):Population of City A at \(t = 4\):\(A(4) = 2 + \frac{5}{12} \times 4 = 2 + \frac{5}{3} \approx 2 + 1.67 = 3.67\) millionPopulation of City B at \(t = 4\):\(B(4) = 2 + \frac{4}{12} \times 4 = 2 + \frac{4}{3} \approx 2 + 1.33 = 3.33\) 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 \(t\) 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 \(t = 0\). Therefore, at \(t = 0\), \(A(t) = B(t)\). 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 \(t\) at which \(A(t) = B(t)\) is true is \(t = 0\).c. To identify values of \(t\) 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 \(t = 0\), City A's population is always greater than City B's population until \(t = 12\). Therefore, any value of \(t\) between 0 and 12 (excluding 0) will satisfy the inequality \(B(t) < A(t)\).Two such values could be \(t = 4\) and \(t = 8\), as examples.Answer: Two values of \(t\) at which \(B(t) < A(t)\) is true are \(t = 4\) and \(t = 8\).